Common Probability Distributions

CFA level I / Quantitative Methods: Application / Common Probability Distributions

Learning Outcome Statements
1. Probability distribution, discrete and continuous random variables
a. define a probability distribution and distinguish between discrete and continuous random variables and their probability functions;

2. Possible outcomes of a specified discrete random variable
b. describe the set of possible outcomes of a specified discrete random variable;

3. Cumulative distribution function
c. interpret a cumulative distribution function;

4. Probabilities of a random variable given its cumulative distribution function
d. calculate and interpret probabilities for a random variable, given its cumulative distribution function;

5. Discrete uniform and binomial distribution functions
e. define a discrete uniform random variable, a Bernoulli random variable, and a binomial random variable;
f. calculate and interpret probabilities given the discrete uniform and the binomial distribution functions;

6. Binomial tree to describe stock price movement
g. construct a binomial tree to describe stock price movement;

7. Calculate and interpret tracking error
h. calculate and interpret tracking error;

8. Continuous uniform distribution
i. define the continuous uniform distribution and calculate and interpret probabilities, given a continuous uniform distribution;

9. Key properties of the normal distribution
j. explain the key properties of the normal distribution;

10. Univariate and multivariate distributions
k. distinguish between a univariate and a multivariate distribution and explain the role of correlation in the multivariate normal distribution;

11. Probability of a normally distributed random variable inside a given interval
l. determine the probability that a normally distributed random variable lies inside a given interval;

12. Standard normal distribution and standardizing a random variable
m. define the standard normal distribution, explain how to standardize a random variable, and calculate and interpret probabilities using the standard normal distribution;

13. Shortfall risk, safety-first ratio, and Roy's safety-first criterion
n. define shortfall risk, calculate the safety-first ratio, and select an optimal portfolio using Roy’s safety-first criterion;

14. Relationship between normal and lognormal distributions
o. explain the relationship between normal and lognormal distributions and why the lognormal distribution is used to model asset prices;

15. Discretely and continuously compounded rates of return
p. distinguish between discretely and continuously compounded rates of return and calculate and interpret a continuously compounded rate of return, given a specific holding period return;

16. Monte Carlo simulation and historical simulation
q. explain Monte Carlo simulation and describe its applications and limitations;
r. compare Monte Carlo simulation and historical simulation.

Common Probability Distributions: Chapter Test
12 Questions, 18 Minutes

    CFA Institute does not endorse, promote or warrant the accuracy or quality of products and services offered by Konvexity. CFA® and Chartered Financial Analyst® are registered trademarks owned by CFA Institute.