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 X = the number of batches ordered by a randomly chosen customer, and suppose that X has the following pmf.

Compute E(X) and V(X).

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.]

x 1 2 3 4 p(x)       0.2     0.5     0.2     0.1  

Explanation / Answer

From the given data,

a) Mean = E(X) = 2.2

Variance = Var(X) = 5.6 - 2.22 = 0.76

b) Let Y = 100 - 8 X

E(X) = 100 - 8 E(X) = 100 - 8*2.2 = 82.4

Var(X) = 82 Var(X) = 64*0.76 = 48.64

X P(X=x) xP(X=x) X^2P(X=x) 1 0.2 0.2 0.2 2 0.5 1 2 3 0.2 0.6 1.8 4 0.1 0.4 1.6 Total: 2.2 5.6

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