Page 70 - FINAL CFA SLIDES DECEMBER 2018 DAY 3

Session Unit 3:
10. Common Probability Distributions

LOS 10.e: Define a Discrete Uniform Random Variable, a Bernoulli random variable, and a binomial random

variable, p.217
LOS 10.f: Calculate and interpret probabilities given the discrete uniform and the binomial distribution functions

A Discrete Uniform Random Variable -p for all possible outcomes are equal.

e.g. X = {1, 2, 3, 4, 5}, p(x) = 0.2, i.e. [i.e., p(1) = p(2) = p(3) = p(4) = p(5) = 0.2].

Also, the CDF for the nth outcome, F(xn) = np(x); and

The p. of a range of outcomes is p(x)k, where k is the no. of possible outcomes in the range.

Answer: p(x) = 0.2 hence p(6) = 0.2 (uniform)

F(xn) = np(x) = F(6) = P(X ≤ 6) = np(x) = 3(0.2) = 0.6.

P(2 ≤ X ≤ 8) = 4(0.2) = 0.8.

Note that k = 4, since there are four outcomes in the
range 2 ≤ X ≤8.