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.