Question

A discrete random variable, X, has the following probability distribution: P(X) lorem What is the probability that X is not more than 1? (b) What is the probability that X is at least 22|| What is the mean of X? (d) What is the standard deviation of X?

Answer 1

a) P(X < 1) = P(X = 0) + P(X = 1) = 0.1 + 0.2 = 0.3

b) P(X > 2) = P(X = 2) + P(X = 3) = 0.4 + 0.3 = 0.7

c) Mean = E(X) = 0 * 0.1 + 1 * 0.2 + 2 * 0.4 + 3 * 0.3 = 1.9

d) E(X²) = 0² * 0.1 + 1² * 0.2 + 2² * 0.4 + 3² * 0.3 = 4.5

Var(X) = E(X²) - (E(X))² = 4.5 - 1.9² = 0.89

Standard deviation = sqrt(0.89) = 0.94