Common Probability Distributions
CFA level I
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Quantitative Methods: Application
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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 |