Probability Concepts

CFA level I / Quantitative Methods: Basic Concepts / Probability Concepts

Learning Outcome Statements

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

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

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

4. Conditional and unconditional probabilities
d. distinguish between unconditional and conditional probabilities;

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

6. Joint probability
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;

7. Dependent and independent events
g. distinguish between dependent and independent events;

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

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

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

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

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

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

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

Probability Concepts: Chapter Test
12 Questions, 18 Minutes