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 3-lb batches. Let X= the number of batches ordered by a randomly chosen customer, and suppose that X has the following pmf. 1 2 3 4 p(x) 0.3 0.4 0.2 0.1 Compute E(X) and V(X) E(X) = | batches 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 inear function of X.] expected weight left variance of weight left lb lb2

Explanation / Answer

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

V(x)= 0.3*(1-2.1)^2+0.4*(2-2.1)^2+0.2*(3-2.1)^2+0.1*(4-2.1)^2=0.89

b)E(weight) = 100-2.1=97.9

V(weight0=V(x)=0.89

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