Page 74 - FINAL CFA SLIDES DECEMBER 2018 DAY 3

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

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

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.
Meaning?
However, if we were to 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.