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.

x 1 2 3 4
p(x) 0.3 0.5 0.1 0.1

Compute E(X) and V(X).

E(X) = batches
V(X) = batches2

Compute the expected number of pounds left after the next customer's order is shipped and the variance of the number of pounds left. [Hint: The number of pounds left is a linear function of X.]

expected weight left lb
variance of weight left lb2