Reference no: EM133245449

A mail-order computer business has seven telephone lines. Let X denote the number of lines in use at a specified time. Suppose the probability mass function (PMF)  of X is as given in the accompanying table. PMF gives the probability that a discrete random variable is exactly equal to some value.

X 0 1 2 3 4 5 6 7

p(X) 0.1 0.15 0.2 0.25 0.15 0.1 0.03 0.02

Calculate the probability of each of the following events.

a. Find and plot the CDF of X.

b. At most three lines are in use

c. Fewer than three lines are in use

d. At least three lines are in use

e. Between two and five lines, inclusive, are in use

f. Between two and four lines, inclusive, are not in use

g. At least four lines are not in use

h. Compute the expected value and variance of X.

i. For each busy line, the operator sends a bill of $0.01 for maintenance service. Find the expected value and variance of the total due amount.