Question

Let the random variable X denote the number of network blackouts in a day. The
probability mass function of X is:
x 0 1 2
P(X ) 0.7, 0.2, 0.1
A small internet trading company estimates that each networkblackout results in a $500 loss.compute expectation and variance of this company 's daily loss due to blackouts

Answer 1

E(X) = 0(0.7) + 1(0.2) + 2(0.1) = 0.2 + 0.2 = 0.4
The expected daily loss due to blackouts = 0.4 * $500 = $200

Var(X) = 0(0.7 - 0.4)^2 + 1(0.2 - 0.4)^2 + 2(0.1 - 0.4)^2 = 0.04 + 0.18 = 0.22
The expected daily variance due to blackouts = 0.22 * $500 = $110