- Writing Learning Objectives
- Examples of Learning Objectives and Learning Outcomes
- Advantages of Creating Learning Objectives
- Testing Questions by Bloom’s Level
- Example: CAS and SOA Learning Objectives for Life Contingency Mathematics
- Partial List of Sources

Learning objectives have three components:

- Noun: what is the thing to learn?
- Level: Bloom’s level
- Observable verb or action verb: behavior at the appropriate level of learning; “At the conclusion of this activity, participants will be able to…” Use verbs which describe an action that can be observed and that are measurable within the teaching time frame (e.g., via a post-test).

**Behavior**- a description of what the learner will be able to do.; Write learning objectives in terms of an observable, behavioral outcome; essentially, learning objectives should provide a description of what the student will be able to do. When writing the objective in performance terminology, the selection of an effective action verb is of utmost importance. The use of a clear, targeted verb provides directions about the expectations of student performance at the completion of instructional activities. Because the verb provides the desired direction of emphasis, it is important to choose a verb that is focused and targets a level of performance appropriate for the course.**Behavior**- First, an objective must describe the competency to be learned in performance terms. The choice of a verb is all-important here. Such frequently used terms as know, understand, grasp, and appreciate do not meet this requirement. If the verb used in stating an objective identifies an observable student behavior, then the basis for a clear statement is established. In addition, the type or level of learning must be identified. See Section II for a description of the types of learning and their levels.**Conditions**: a description of conditions under which the student will perform the behavior.; Learning objectives should be specific and target one expectation or aspect of understanding and highlight the conditions under which the student is expected to perform the task. The conditions of the objective should communicate the situation, tools, references, or aids that will be provided for the student.**Conditions**- Third, an objective should describe the conditions under which the learner will be expected to perform in the evaluation situation. What tools, references, or other aids will be provided or denied should be made clear.**Condition**:**when**will you be able to do it?**Criterion**or**Standards**: the quality or level of performance that will be considered acceptable.; Each learning objective should be measurable and include the criteria for evaluating student performance. Generally, standards provide information to clarify to what extent a student must perform to be judged adequate; thus effective learning objectives indicate a degree of accuracy, a quantity of correct responses or some other type of measurable information. Standards serve the dual purpose of informing students of performance expectations and providing insight as to how achievement of these expectations will be measured. Since students will utilize the standards to guide their performance, be sure to use specific terminology that has limited interpretations and ensure that all students understand the same interpretation.**Criterion**- Second, an objective should make clear how well a learner must perform to be judged adequate. This can be done with a statement indicating a degree of accuracy, a quantity or proportion of correct responses or the like.**Student-Centered**- All learning objectives should focus on the student. An effective learning objective will explain expectations for student behavior, performance, or understanding. To ensure that learning objectives are student centered, a good objective should appropriately complete the statement “The student will…”Example: “Given a set of data the student will be able to compute the standard deviation.”

- Condition - Given a set of data
- Behavior - the student will be able to compute the standard deviation.
- Criterion - (implied) - the number computed will be correct.

Learning objectives have two parts: an

**action verb**and a**content area**. Utilize the action verb to specify the desired student performance followed by a specific description of the course-specific content target.Keep statements

**short**and focused on a single outcome. This allows instructors to determine whether or not an objective has been met without having to distinguish between partial completion or success.To ensure that learning objectives are effective and measurable, avoid using verbs that are vague or cannot be objectively assessed. Use active verbs that describe what a student will be able to do once learning has occurred.

Learning objectives should be student-focused and target the expected student outcome. To assist in maintaining a student-centered emphasis, start learning objectives with the phrase “

**The learner/student will be able to…**”Learning objectives should be SMART (specific, measurable, acceptable to the instructor, realistic to achieve, and time-bound with a deadline).

Include complex or higher-order learning objectives when they are appropriate. Most instructors expect students to go beyond memorization of facts and terminology; learning objectives should reflect instructors’ expectations for student performance.

Utilize learning objectives as a

**basis for course preparation**. Learning objectives should match instructional strategies and assessment requirements. To ensure the connection between various course activities, it is useful to construct a table highlighting the relationship. For example:

Emphasis | Relevant Verbs |
---|---|

Knowledge | Recall, identify, recognize, acquire, distinguish, state, define, name, list, label, reproduce, order |

Remembering | The students will recall the four major food groups without error. |

Comprehension | Translate, extrapolate, convert, interpret, abstract, transform, select, indicate, illustrate, represent, formulate, explain, classify, comprehend |

Understanding | The students will summarize the main events of a story in grammatically correct English. |

Application | Apply, sequence, carry out, solve, prepare, operate, generalize, plan, repair, explain, predict, demonstrate, instruct, compute, use, perform, implement, employ, solve |

Applying | The students will multiply fractions in class with 90% accuracy. |

Analysis | Analyze, estimate, compare, observe, detect, classify, discover, discriminate, explore, distinguish, catalog, investigate, breakdown, order, determine, differentiate, dissect, contrast, examine, interpret |

Analyzing | Students will discriminate among a list of possible steps to determine which one(s) would lead to increased reliability for a testing a concept. |

Synthesis | Write, plan, integrate, formulate, propose, specify, produce, organize, theorize, design, build, systematize, combine, summarize, restate, argue, discuss, derive, relate, generalize, conclude, produce |

Creating | After studying the current economic policies of the United States, student groups will design their own fiscal and monetary policies. |

Evaluation | Evaluate, verify, assess, test, judge, rank, measure, appraise, select, check, judge, justify, evaluate, determine, support, defend, criticize, weigh, assess |

Evaluating | Evaluate the appropriateness of the conclusions reached in a research study based on the data presented. |

- Students will be able to
**collect**and**organize**appropriate clinical data (history, physical exam, laboratory assessments including technology advancements in diagnostic such as PCR). - Students will be able to
**apply**principles of evidence-based medicine to determine clinical diagnoses, and formulate and implement acceptable treatment modalities. - Students will be able to
**articulate**cultural and socioeconomic differences and the significance of these differences for instructional planning. - Students will be able to
**use technology**effectively in the delivery of instruction, assessment, and professional development. - Students will be able to
**evaluate**the need for assistance technology for their students. - Graduates will be able to
**evaluate**educational research critically and participate in the research community. - Students will appreciate the value of outcomes assessment in assuring quality across the veterinary medical profession and in facilitating movement of the veterinary medical professionals across national borders.

- Bad verbs: hard to test
- know familiarize gain knowledge of comprehend study cover understand be aware learn appreciate become acquainted with realize
- appreciate believe improve learn approach grasp the significance of increase thinks critically become grow know understand

COVERT | OVERT |
---|---|

Understand Ohm’s Law | Define Ohm’s Law in writing |

Determine the bad circuit | Verbally identify the bad circuit |

Select between… | Sort into groups |

Original version: Understand the American criminal justice system.

Revised version: Describe the history of the American criminal justice system.

Original version: Describe and create a social media plan for your organization.

Revised version: Create a social media plan for your organization.

Learning outcomes are not about what the instructors can provide but what the students can demonstrate. The following are **not** learning outcomes:

- Offer opportunities for students to master integrated use of information technology.
- The program will engage a significant number of students in a formalized language/cultural studies program.
- Students who participate in critical writing seminars will write two essays on critical thinking skills.

Learning objectives allow you to:

plan the sequence for instruction, allocate time to topics, assemble materials and plan class outlines.

develop a guide to teaching allowing you to plan different instructional methods for presenting different parts of the content. (e.g. small group discussions of a common misconception).

facilitate various evaluation activities, evaluating students, evaluating instruction and even evaluating the curriculum.

A learning objective answers the question: What is it that your students should be able to do at the end of the class session and course that they could not do before?

A learning objective makes clear the intended learning outcome rather than what form the instruction will take.

Learning objectives focus on student performance. Action verbs that are specific, such as list, describe, report, compare, demonstrate, and analyze, should state the behaviors students will be expected to perform

Verb | Explanation |
---|---|

Knowledge | to recall or remember facts without necessarily understanding them |

Comprehension | to understand and interpret learned information |

Application | to put ideas and concepts to work in solving problems |

Analysis | to break information into its components to see interrelationships and ideas |

Synthesis | to use creativity to compose and design something original |

Evaluation | to judge the value of information based on established criteria |

Knowledge | Understand | Apply | Analyze | Evaluate | Create |
---|---|---|---|---|---|

define | explain | solve | analyze | reframe | design |

identify | describe | apply | compare | criticize | compose |

describe | interpret | illustrate | classify | evaluate | create |

label | paraphrase | modify | contrast | order | plan |

list | summarize | use | distinguish | appraise | combine |

name | classify | calculate | infer | judge | formulate |

state | compare | change | separate | support | invent |

match | differentiate | choose | explain | compare | hypothesize |

recognize | discuss | demonstrate | select | decide | substitute |

select | distinguish | discover | categorize | discriminate | write |

examine | extend | experiment | connect | recommend | compile |

locate | predict | relate | differentiate | summarize | construct |

memorize | associate | show | discriminate | assess | develop |

quote | contrast | sketch | divide | choose | generalize |

recall | convert | complete | order | convince | integrate |

reproduce | demonstrate | construct | point out | defend | modify |

tabulate | estimate | dramatize | prioritize | estimate | organize |

tell | express | interpret | subdivide | find errors | prepare |

copy | identify | manipulate | survey | grade | produce |

discover | indicate | paint | advertise | measure | rearrange |

duplicate | infer | prepare | appraise | predict | rewrite |

enumerate | relate | produce | break down | rank | role-play |

listen | restate | report | calculate | score | adapt |

observe | select | teach | conclude | select | anticipate |

omit | translate | act | correlate | test | arrange |

read | ask | administer | criticize | argue | assemble |

recite | cite | articulate | deduce | conclude | choose |

record | discover | chart | devise | consider | collaborate |

repeat | generalize | collect | diagram | critique | collect |

retell | give examples | compute | dissect | debate | devise |

visualize | group | determine | estimate | distinguish | express |

illustrate | develop | evaluate | editorialize | facilitate | |

judge | employ | experiment | justify | imagine | |

observe | establish | focus | persuade | infer | |

order | examine | illustrate | rate | intervene | |

report | explain | organize | weigh | justify | |

represent | interview | outline | make | ||

research | judge | plan | manage | ||

review | list | question | negotiate | ||

rewrite | operate | test | originate | ||

show | practice | propose | |||

trace | predict | reorganize | |||

transform | record | report | |||

schedule | revise | ||||

simulate | schematize | ||||

transfer | simulate | ||||

write | solve | ||||

speculate | |||||

structure | |||||

support | |||||

test | |||||

validate |

Knowledge | Comprehension | Application | Analysis | Synthesis | Evaluation |
---|---|---|---|---|---|

List Name Identify Show Define Recognize Recall State Visualize | Summarize Explain Interpret Describe Compare Paraphrase Differentiate Demonstrate Classify | Solve Illustrate Calculate Use Interpret Relate Manipulate Apply Modify | Analyze Organize Deduce Contrast Compare Distinguish Discuss Plan Devise | Design Hypothesize Support Schematize Write Report Justify | Evaluate Choose Estimate Judge Defend Criticize |

Level Attributes | Keywords | Questions |
---|---|---|

Exhibits previously learned material by recalling facts, terms, basic concepts and answers. | who, what, why, when, omit, where, which, choose, find, how, define, label, show, spell, list, match, name, relate, tell, recall, select | What is …? How is …? Where is …? When did _______ happen? How did ______ happen? How would you explain …? Why did …? How would you describe …? When did …? Can you recall …? How would you show …? Can you select …? Who were the main …? Can you list three …? Which one …? Who was …? |

Level Attributes | Keywords | Questions |
---|---|---|

Demonstrating understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions and stating main ideas. | compare, contrast, demonstrate, interpret, explain, extend, illustrate, infer, outline, relate, rephrase, translate, summarize, show, classify | How would you classify the type of …? How would you compare …? contrast …? Will you state or interpret in your own words …? How would you rephrase the meaning …? What facts or ideas show …? What is the main idea of …? Which statements support …? Can you explain what is happening . . . what is meant . . .? What can you say about …? Which is the best answer …? How would you summarize …? |

Level Attributes | Keywords | Questions |
---|---|---|

Solving problems by applying acquired knowledge, facts, techniques and rules in a different way. | apply, build, choose, construct, develop, interview, make use of, organize, experiment with, plan, select, solve, utilize, model, identify | How would you use …? What examples can you find to …? How would you solve _______ using what you have learned …? How would you organize _______ to show …? How would you show your understanding of …? What approach would you use to …? How would you apply what you learned to develop …? What other way would you plan to …? What would result if …? Can you make use of the facts to …? What elements would you choose to change …? What facts would you select to show …? What questions would you ask in an interview with …? |

Level Attributes | Keywords | Questions |
---|---|---|

Examining and breaking information into parts by identifying motives or causes; making inferences and finding evidence to support generalizations. | analyze, categorize, classify, compare, contrast, discover, dissect, divide, examine, inspect, simplify, survey, take part in, test for, distinguish, list, distinction, theme, relationships, function, motive, inference, assumption, conclusion | What are the parts or features of …? How is _______ related to …? Why do you think …? What is the theme …? What motive is there …? Can you list the parts …? What inference can you make …? What conclusions can you draw …? How would you classify …? How would you categorize …? Can you identify the difference parts …? What evidence can you find …? What is the relationship between …? Can you make a distinction between …? What is the function of …? What ideas justify …? |

Level Attributes | Keywords | Questions |
---|---|---|

Compiling information together in a different way by combining elements in a new pattern or proposing alternative solutions. | build, choose, combine, compile, compose, construct, create, design, develop, estimate, formulate, imagine, invent, make up, originate, plan, predict, propose, solve, solution, suppose, discuss, modify, change, original, improve, adapt, minimize, maximize, delete, theorize, elaborate, test, improve, happen, change | What changes would you make to solve …? How would you improve …? What would happen if …? Can you elaborate on the reason …? Can you propose an alternative …? Can you invent …? How would you adapt ________ to create a different …? How could you change (modify) the plot (plan) …? What could be done to minimize (maximize) …? What way would you design …? What could be combined to improve (change) …? Suppose you could _______ what would you do …? How would you test …? Can you formulate a theory for …? Can you predict the outcome if …? How would you estimate the results for …? What facts can you compile …? Can you construct a model that would change …? Can you think of an original way for the …? |

Level Attributes | Keywords | Questions |
---|---|---|

Presenting and defending opinions by making judgments about information, validity of ideas or quality of work based on a set of criteria. | award, choose, conclude, criticize, decide, defend, determine, dispute, evaluate, judge, justify, measure, compare, mark, rate, recommend, rule on, select, agree, interpret, explain, appraise, prioritize, opinion, ,support, importance, criteria, prove, disprove, assess, influence, perceive, value, estimate, influence, deduct | Do you agree with the actions …? with the outcomes …? What is your opinion of …? How would you prove …? disprove …? Can you assess the value or importance of …? Would it be better if …? Why did they (the character) choose …? What would you recommend …? How would you rate the …? What would you cite to defend the actions …? How would you evaluate …? How could you determine …? What choice would you have made …? What would you select …? How would you prioritize …? What judgment would you make about …? Based on what you know, how would you explain …? What information would you use to support the view …? How would you justify …? What data was used to make the conclusion …? Why was it better that …? How would you prioritize the facts …? How would you compare the ideas …? people …? |

Recognizes students’ ability to use rote memorization and recall certain facts.

Action verbs to help write objectives or exam questions for this domain: cite, define, identify, label, list, match, name, recognize, reproduce, select, state.

Learning objectives | Exam questions |
---|---|

The students will recall the four major food groups without error. | Name the four major food groups. |

The students will list at least three characteristics peculiar to the Cubist movement. | List three characteristics that are unique to the Cubist movement. |

The students will be able to define grampositive bacteria. | Define gram-positive bacteria. |

Involves students’ ability to read course content, understand and interpret important information and put other’s ideas into their own words.

Action verbs to help write objectives or exam questions for this domain: classify, convert, describe, distinguish between, explain, extend, give examples, illustrate, interpret, paraphrase, summarize, translate.

Learning objectives | Exam questions |
---|---|

The students will summarize the main events of a story in grammatically correct English. | Using grammatically correct English, please summarize the main events – in three or four sentences - from the news story given below. |

The students will describe in prose what is shown in graph form. | Given a graph of production trends in automobiles, describe what the graph represents in a memo to your boss. |

From a “story-problem” description, students will convert the story to a mathematical manipulation needed to solve the problem. | A researcher wonders whether attending a private high school leads to higher or lower performance on an exam of social skills. A random sample of 100 students from a private school produces a mean score of 71.30 on the exam, and the national mean score for students from public schools is 75.62 (s x = 29.0). Convert the information in this word problem into a mathematical representation that will enable you to solve the problem. |

Students take new concepts and apply them to another situation.

Action verbs to help write objectives or exam questions for this domain: apply, arrange, compute, construct, demonstrate, discover, modify, operate, predict, prepare, produce, relate, show, solve, use.

Learning objectives | Exam questions |
---|---|

The students will multiply fractions in class with 90 percent accuracy. | Solve for the ten following fraction multiplication problems. Please make sure to show all your work. |

The students will apply previously learned According to our definition of socialism, information about socialism to reach an answer. | According to our definition of socialism, which of the following nations would be considered to be socialist? |

The students will demonstrate the principle of reinforcement to classroom interactions. | In a teaching simulation with your peers role-playing 6th grade students, demonstrate the principle of reinforcement in classroom interactions and prepare a ½ page description of what happened during the simulation that validated the principle. |

Students have the ability to take new information and break it down into parts to differentiate between them.

Action verbs to help write objectives or exam questions for this domain: analyze, associate, determine, diagram, differentiate, discriminate, distinguish, estimate, infer, order, outline, point out, separate, subdivide.

Learning objectives | Exam questions |
---|---|

The students will read a presidential debate and point out the passages that attack a political opponent personally rather than the opponent’s political programs. | From the short presidential debate transcribed below: Differentiate the passages that attacked a political opponent personally, and those that attacked an opponent’s political programs. |

The students will point out the positive and negative points presented in an argument for the abolition of guns. | From the argument given below, analyze the positive and negative points presented concerning the abolition of guns and write a brief (2-3 page) narrative of your analysis. |

Students will discriminate among a list of possible steps to determine which one(s) would lead to increased reliability for a test. | Determine which of the following steps would most likely lead to an increase in the reliability estimate for a test: a. Increasing the number of persons tested from 500 to 1,000. b. Selecting items so that half were very difficult and half very easy c. Increasing the length of the test with more of the same kinds of items d. Increasing the homogeneity of the group of subjects tested. |

Students are able to take various pieces of information and form a whole creating a pattern where one did not previously exist.

Action verbs to help write objectives or exam questions for this domain: combine, compile, compose, construct, create, design, develop, devise, formulate, integrate, modify, organize, plan, propose, rearrange, reorganize, revise, rewrite, tell, write.

Learning objectives | Exam questions |
---|---|

The students will write a different but plausible ending to a short story. | Develop one plausible ending for all three short stories below. |

After studying the current economic policies of the United States, student groups will design their own goals for fiscal and monetary policies. | Working in your groups and considering the current economic policies of the US that we have been studying, develop your goals for employment, price levels, and rate of real economic growth for the next three years. Write these goals on the newsprint and be ready to discuss why your goals are feasible. |

The students will design a series of chemical operations to separate quantitatively the elements in a solution. | In the lab, you will be given a solution to analyze to see what elements make up the solution. Then design a series of chemical operations to separate quantitatively the elements in the solution. |

Involves students’ ability to look at someone else’s ideas or principles and see the worth of the work and the value of the conclusions.

Action verbs to help write objectives or exam questions for this domain: appraise, assess, compare, conclude, contrast, criticize, discriminate, evaluate, judge, justify, support, weigh. Writing Learning Objectives 9 | Page

Learning objectives | Exam questions |
---|---|

The students will use the principles of socialism to evaluate the US economic system. | Using the basic principles of socialism discussed in this course, evaluate the US economic system by providing key arguments to support your judgment. |

Given any research study, evaluate the appropriateness of the conclusions reached based on the data presented. | For years, misinformation about negative effects of aspartame has proliferated on the internet. The committee evaluated peerreviewed research from the scientific literature on this topic and concluded: “Aspartame consumption is not associated with adverse effects in the general population”. – Given the data we’ve looked at on this topic, evaluate how appropriate this conclusion is and defend your answer. |

The students will compare two pieces of sculpture, giving reasons for their positive evaluation of one over the other. | Two pieces of sculpture from different eras and artists are displayed. Study these two pieces, use the compare-contrast method to determine which piece you prefer and write a 2-3 page report that describes your thinking process as you studied these pieces. Utilize the skills you have learned as we have studied various pieces of sculpture over the past two weeks. |

Range of weight for Section A: 65-70 percent

Candidates should be able to work with discrete and continuous univariate probability distributions for failure time random variables. They will be expected to set up and solve equations in terms of life table functions, cumulative distribution functions, survival functions, probability density functions, and hazard functions (e.g., force of mortality), as appropriate. They should have similar facility with models of the joint distribution of two failure times (multiple lives) and the joint distribution of competing risks (multiple decrement). Candidates should be able to use Markov Chains in order to determine state probabilities and transition probabilities.

**A.1.** For discrete and continuous univariate probability distributions for failure time random variables, develop expressions in terms of the life table functions, *l*_{x}, *q*_{x}, *p*_{x}, _{n}*q*_{x}, _{n}*p*_{x}, and _{m|n}*q*_{x}, for the cumulative distribution function, the survival function, the probability density function and the hazard function (force of mortality), and be able to:

- Establish relations between the different functions
- Develop expressions, including recursion relations, in terms of the functions for probabilities and moments associated with functions of failure time random variables, and calculate such quantities using simple failure time distributions

The distributions may be left-truncated, right-censored, both, or neither.

Range of weight: 10-20 percent

READINGS Cunningham et al., Chapters 5.1-5.3 and 6.1-6.4 Spring and Fall 2015 Exam LC Syllabus Exam LC-2

- Failure time random variables
- Life table functions
- Cumulative distribution functions
- Survival functions
- Probability density functions
- Hazard functions
- Relationships between failure time random variables in the functions above

**A.2.** Assuming a uniform distribution of deaths, define the continuous survival time random variable that arises from the discrete survival time random variable.

Range of weight: 5-10 percent

READINGS Cunningham et al., Chapter 6.6

- Life table function forms under uniform distribution of deaths assumption

**A.3.** Given the joint distribution of two failure times:

Calculate probabilities and moments associated with functions of these random variables’ variances.

Characterize the distribution of the smaller failure time (the joint life status) and the larger failure time (the last survivor status) in terms of functions analogous to those in the Learning Objective 1 above, as appropriate.

Develop expressions, including recursion relations, for probabilities and moments of functions of the joint life status and the last survivor status, and express these in terms of the univariate functions in Learning Objective A1 above (assuming independence of the two failure times).

Range of weight: 10-20 percent

READINGS Cunningham et al., Chapters 12.1-12.2 and 12.6

- Joint distribution of failure times
- Probabilities and moments

**A.4.** Based on the joint distribution (pdf and cdf) of the time until failure and the cause of failure in the competing risk (multiple decrement) model and in terms of the functions *l*_{x}^{(t)}, _{t}*q*_{x}^{(t)}, _{t}*p*_{x}^{(t)}, [**_{t}*d*_{x}^{(t)}]{.math .inline}:

Establish relations between the functions.

Calculate probabilities and moments associated with functions of these random variables, given the joint distribution of the time of failure and the cause of failure.

Note: Candidates will not be tested on the absolute rate of death (*q*_{x}’^{(1)})

Range of weight: 10-20 percent

READINGS Cunningham et al., Chapters 13.1-13.3 Spring and Fall 2015 Exam LC Syllabus Exam LC-3

- Time until failure
- Competing risk (multiple decrement) models

**A.5.** For homogenous and non-homogenous discrete-time Markov chain models:

Define each model.

Calculate probabilities of being in a particular state at a particular time.

Calculate probabilities of transitioning between states.

Range of weight: 10-20 percent

READINGS Daniel Markov, Chapters 1 and 3

- Markov chains
- Transition probability matrix
- Discrete-time Markov chains

Range of weight for Section B: 30-35 percent

**B.1.** Apply a principle to a present value model to associate a cost or pattern of costs (possibly contingent) with a set of future contingent cash flows.

Range of weight: 20-25 percent

READINGS Cunningham et al., Chapters 7.1-7.3, 8.1-8.3, 9.1.1-9.1.3, 9.2, and 9.4

- Principles include: equivalence, exponential, standard deviation, variance, and percentile
- Models including those listed in Learning Objective A: Survival Models.
- Principle applications include: life insurance, annuities, health care, credit risk, environmental risk, consumer behavior (e.g., subscriptions), and warranties

**B.2.** Using present-value-of-benefit random variables extended to discrete time Markov chains, calculate:

Actuarial present values of cash flows at transitions between states

Actuarial present values of cash flows while in a state

Considerations (premiums) using the Equivalence Principle

Range of weight: 5-15 percent

READINGS Daniel Markov, Chapters 2 and 3

- Cash flows at transition
- Triple product summation
- Transition probabilities

MLC = modeling life contingencies, which is concerned with the pricing and reserving of long-duration insurance contracts typically covering an insured life. Examples: term, whole and universal life, endowment insurance, annuities, pensions.

The Candidate will understand key concepts concerning tabular or parametric survival models and single or multiple-life states.

The Candidate will be able to:

- Explain and interpret the effects of transitioning between states, the survival models and their interactions. Calculate and interpret standard probability functions including survival and mortality probabilities, force of mortality, and complete and curtate expectation of life.
- For models dealing with multiple lives and/or multiple states, explain the random variables associated with the model; calculate and interpret marginal and conditional probabilities, and moments.
- Using the factors mentioned in Learning Outcomes 1a and 1b, construct and interpret survival models for cohorts consisting of non-homogeneous populations, for example, smokers and non-smokers or ultimate-and-select groups.
- Describe the behavior of continuous-time and discrete-time Markov chain models, identify possible transitions between states, and calculate and interpret the probability of being in a particular state and transitioning between states.
- Apply to calculations involving these models appropriate approximation methods such as uniform distribution of deaths, constant force, Woolhouse, and Euler.

The Candidate will be able to perform calculations on the present value random variables associated with benefits and expenses for any of the models mentioned in the Learning Outcomes of Learning Objective 1.

The Candidate will be able to:

- Calculate and interpret probabilities, means, percentiles and higher moments.
- Calculate and interpret the effect of changes in underlying assumptions such as mortality and interest.
- Apply to calculations involving these random variables appropriate approximation methods such as uniform distribution of deaths, constant force, Woolhouse, and Euler.

The Candidate will be able to both calculate with and explain premium-calculation methodologies such as the equivalence principle, the portfolio-premium principle, and premiums determined by specified profit objectives.

The Candidate will be able to:

- Calculate and interpret probabilities, means, percentiles and higher moments of random variables associated with these premiums, including loss-at-issue random variables.
- Using any of the models mentioned in the Learning Outcomes of Learning Objective 1, calculate and interpret the effect of changes in policy design and underlying assumptions such as changes in mortality, benefits, expenses, interest and dividends.
- Perform the calculations mentioned in Learning Outcomes 3a and 3b for contracts associated with specified contingent cash flows including
- Non-interest-sensitive insurances;
- Annuities;
- Universal life insurances; and
- Participating insurances.

- Apply to calculations involving these premiums appropriate approximation methods such as uniform distribution of deaths, constant force, Woolhouse, and Euler

The Candidate will understand reserves for insurances and annuities for models mentioned in the Learning Outcomes of Learning Objectives 1 and 3.

The Candidate will be able to:

- Calculate and interpret any of (i) several reserve types including benefits reserves, gross premium reserves, expense reserves or any of (ii) several reserve methods such as Full Preliminary Term (FPT) or modified reserves.
- Calculate and interpret probabilities, means, percentiles and higher moments of random variables associated with these reserves, including future-loss random variables.
- Calculate and interpret asset shares, expected profit, actual profit, gain, gain by source and period, internal rate of return and other common profit measures.
- Calculate and interpret the effect of policy modifications.
- Calculate and interpret contract account values, contract surrender values and profit measures on universal life insurance contracts.
- Compare and contrast non-interest-sensitive and participating insurances with universal life insurances.
- Calculate and interpret the effect of changes in policy design and underlying assumptions such as changes in mortality, benefits, expenses, interest and dividends.
- Apply to calculations involving these reserves appropriate approximation methods such as uniform distribution of deaths, constant force, Woolhouse, and Euler.

The Candidate will understand how the models from previous Learning Objectives apply to pension plans and retirement benefits.

The Candidate will be able to:

- Describe and compare defined contribution and defined benefit pension plans including final salary and career average earning plans.
- Identify and interpret the common states and decrements for pension plans, and the parametric and tabular models, including Markov chain models, associated with these decrements.
- Given particular participant data, plan provisions, and valuation assumptions, apply the models mentioned in learning outcome 5b to defined benefit pension plans and calculate and interpret replacement ratios, accrued benefits, and their expected values with adjustments such as the early retirement reduction factor.
- Given particular participant data, plan provisions, and valuation assumptions, calculate and interpret the actuarial accrued liability and the normal cost for a defined benefit plan under the projected unit credit (PUC) cost method and the traditional unit credit (TUC) cost method.
- Calculate and interpret the effect of changes in underlying valuation assumptions such as mortality, salary increase changes, other decrements and interest on the quantities mentioned in learning outcomes 5c and 5d.
- Apply to calculations involving these defined benefit pension plans appropriate approximation methods such as uniform distribution of deaths, constant force, Woolhouse, and Euler.

- https://assessment.trinity.duke.edu
- http://www.gavilan.edu/research/spd/Writing-Measurable-Learning-Outcomes.pdf
- https://i0.wp.com/teachonline.asu.edu/
- https://www.cte.cornell.edu/