Learning Outcome Statements

1. Introduction

a. define a random variable, an outcome, an event, mutually exclusive events, and exhaustive events;

b. state the two defining properties of probability and distinguish among empirical, subjective, and a priori probabilities;

c. state the probability of an event in terms of odds for and against the event;

2. Unconditional, Conditional, and Joint Probabilities

d. distinguish between unconditional and conditional probabilities;

3. Addition Rule for Probabilities: the Probability that at Least One of Two Events Will Occur

e. explain the multiplication, addition, and total probability rules;

f. calculate and interpret 1) the joint probability of two events, 2) the probability that at least one of two events will occur, given the probability of each and the joint probability of the two events, and 3) a joint probability of any number of independent events.

g. distinguish between dependent and independent events;

4. Multiplication Rule for Independent Events

e. explain the multiplication, addition, and total probability rules;

f. calculate and interpret 1) the joint probability of two events, 2) the probability that at least one of two events will occur, given the probability of each and the joint probability of the two events, and 3) a joint probability of any number of independent events.

g. distinguish between dependent and independent events;

5. The Total Probability Rule

h. calculate and interpret an unconditional probability using the total probability rule;

i. explain the use of conditional expectation in investment applications;

j. explain the use of a tree diagram to represent an investment problem;

6. Expected Value, Variance, and Standard Deviation of a Random Variable

l. calculate and interpret the expected value, variance, and standard deviation of a random variable and of returns on a portfolio;

7. Covariance and Correlation

k. calculate and interpret covariance and correlation;

8. Portfolio Expected Return and Variance

m. calculate and interpret covariance given a joint probability function;

9. Bayes' Formula

n. calculate and interpret an updated probability using Bayes' formula;

10. Principles of Counting

o. identify the most appropriate method to solve a particular counting problem and solve counting problems using the factorial, combination, and permutation concepts.