Question

Suppose there are 26 balls in a container, 4 of them are blue and the rest are white, let’s say we draw 3 of them, what is the distribution of P[X = 0] ,P[X=1] , P[X=2] ,and P[X=3], the E[X] and standard deviation?

X being blue balls

Answer 1

P(X = 0) = 22C3/26C3 = 0.5923

P(X = 1) = (4C1 * 22C2)/26C3 = 0.3554

P(X = 2) = (4C2 * 22C1)/26C3 = 0.0508

P(X = 3) = 4C3/26C3 = 0.0015

E(X) = 0 * 0.5923 + 1 * 0.3554 + 2 * 0.0508 + 3 * 0.0015 = 0.4615

E(X^2) = 0^2 * 0.5923 + 1^2 * 0.3554 + 2^2 * 0.0508 + 3^2 * 0.0015 = 0.5721

Variance = E(X^2) - (E(X))^2

= 0.5721 - (0.4615)^2 = 0.3591

Standard deviation = sqrt(0.3591) = 0.5992