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 pmf Compute E(X) and V(X). Then 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.]

Solution : Step 1: It is given that a chemical supply company currently have a stock 100 lb of a certain chemical, which it sells to customers in 5-lb batches. If X= the number of batches ordered by a randomly chosen customer and X has pmf