A new cellular phone billing plan costs $15 per month plus $1 for each minute of use. If the number of minutes you use the phone in a month is a geometric random variable with mean 1/p, what is the expected monthly cost E[C] of the phone? For what values of p is this billing plan preferable to the billing plan of Problem 2.6.6 and Problem 2.7.5?
Problem 2.6.6
Suppose that a cellular phone costs $20 per month with 30 minutes of use included and that each additional minute of use costs $0.50. If the number of minutes you use in a month is a geometric random variable M with expected value of E[M] = 1/p = 30 minutes, what is the PMF of C, the cost of the phone for one month?
Problem 2.7.5
For the cellular phone in Problem 2.6.6, express the monthly cost C as a function of M, the number of minutes used. What is the expected monthly cost E[C]?