A chemical supply company currently has in stock 100 lb of a certain chemical, w

Question

A chemical supply company currently has in stock 100 lb of a certain chemical, which it sells to customers in 8-lb batches. Let Xthe number of batches ordered by a randomly chosen customer, and suppose that X has the following pmf. 1 2 34 p(x) 0.3 0.5 0 0.1 Compute E(x) and V(x) E(x) 2 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 left. [Hint: The number of pounds left is a linear function of X.] expected weight left 8 variance of weight left 32 lb

Explanation / Answer

E(x) = 1 * 0.3 + 2 * 0.5 + 3 * 0.1 + 4 * 0.1

= 2.

V(x) = 1 * 0.3 + 4 * 0.5 + 9 * 0.1 + 16 * 0.1 - 2 * 2

= 0.8.

Expected weight left = 100 - 2 * 8 = 84.

Variance of expected weight left = 10000 - 0.8 * 64 = 9948.8.

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