- CFA Exams
- Dec. 2020 Level 1
- Study Session 3. Quantitative Methods: Application
- Reading 9. Common Probability Distributions
Reading 9. Common Probability Distributions
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Learning Outcome Statements
| Reading 9. Common Probability Distributions | |
|---|---|
| 1. Basic Definitions a. define a probability distribution and distinguish between discrete and continuous random variables and their probability functions; b. describe the set of possible outcomes of a specified discrete random variable; | |
| 2. Probability Function c. interpret a cumulative distribution function; d. calculate and interpret probabilities for a random variable, given its cumulative distribution function; | |
| 3. Cumulative Distribution Function c. interpret a cumulative distribution function; d. calculate and interpret probabilities for a random variable, given its cumulative distribution function; | |
| 4. The Discrete Uniform Distribution 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; g. construct a binomial tree to describe stock price movement; h. calculate and interpret tracking error; i. define the continuous uniform distribution and calculate and interpret probabilities, given a continuous uniform distribution; | |
| 5. The Binomial Distribution 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; g. construct a binomial tree to describe stock price movement; h. calculate and interpret tracking error; i. define the continuous uniform distribution and calculate and interpret probabilities, given a continuous uniform distribution; | |
| 6. The Normal Distribution j. explain the key properties of the normal distribution; | |
| 7. The Univariate and Multivariate Distributions k. distinguish between a univariate and a multivariate distribution and explain the role of correlation in the multivariate normal distribution; | |
| 8. The Standard Normal Distribution l. determine the probability that a normally distributed random variable lies inside a given interval; m. define the standard normal distribution, explain how to standardize a random variable, and calculate and interpret probabilities using the standard normal distribution; | |
| 9. Shortfall Risk 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; | |
| 10. The Lognormal Distribution o. explain the relationship between normal and lognormal distributions and why the lognormal distribution is used to model asset prices; | |
| 11. 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; | |
| 12. Monte Carlo Simulation q. explain Monte Carlo simulation and describe its applications and limitations; r. compare Monte Carlo simulation and historical simulation. |