Page 42 - FINAL CFA I SLIDES JUNE 2019 DAY 3

LOS 10.e: Define a Discrete Uniform Random Session Unit 3:
Variable, a Bernoulli random variable, and a binomial
random variable. 10. Common Probability Distributions ©

LOS 10.f: Calculate and interpret probabilities given the discrete uniform and the binomial DF

Expected Value and Variance of a Binomial Random Variable, p.219

For a given series of n trials, the expected number of successes, or E(X) = np

Variance of X = np – np2 i.e. np(1 – p)
Further, assume that movements in the DJIA are independent
Example: Per empirical data, the p that the DJIA will increase on (i.e., an increase in one day is independent of what happened on
any given day = 0.67. Assuming that the only other outcome is another day). Compute the EV of the number of up days in a
5-day period.
that it decreases.

Answer: UP, so p = 0.67 | p(DOWN) = 0.33 . E(X | n = 5, p = 0.67) = np = (5)(0.67) = 3.35

Since the binomial distribution is a discrete, the result X = 3.35 is not possible. However, if we were to
Meaning?
record the results of many 5-day periods, the average no. of up days (successes) would converge to 3.35.

C. Success = passing the exam. Then, E(success) = np = 15 × 0.4 = 6.