Question

A chemical supply company currently has in stock 100 lb of a certain chemical, which it sells to customers in 5-lb batches. Let X-the number of batches ordered by a randomly chosen customer, and suppose that X has the following pmf 4 p(x)0.3 0.40.2 0.1 Compute E(X) and Vx) E(X) = batches batches Compute the expected number of pounds left after the next customer's order is shipped and the variance of the number of pounds ie expected weight left variance of weight left : The number of pounds e s ain ear function of . lb Ib2

Answer 1

a) E(X) = 1 * 0.3 + 2 * 0.4 + 3 * 0.2 + 4 * 0.1 = 2.1

b) E(X²) = 1^2 * 0.3 + 2^2 * 0.4 + 3^2 * 0.2 + 4^2 * 0.1 = 5.3

V(X) = (E(X)²) - (E(X))^2

       = 5.3 - (2.1)^2

      = 0.89