Question

For the telephone usage model of Example 1.18, let Bm denote the event that a call is billed for m minutes. To generate a phone bill, observe the duration of the call in integer minutes (rounding up). Charge for M minutes M = 1,2, 3, ... if the exact duration T is M-1< t (a) Classify lasts more than three minutes. What is P[L? a call as long, L, if the call
(b) What is the probability that a call will be billed for nine minutes or less?

Answer 1

Answer and  explanation:

(a) Classify a call as long, lasts more than three minutes. What is P [L)?

Given probability of event a call lasts more than three minutes, M the probability and B is denoted as the event that a call is billed minutes.

P (L) = 1 – P (3 or less than three minutes)

        =1 – P (Bm) – P (Bm) –P (Bm)                                for m=1,2,3

         =1 – P(B1) – P(B2) – P(B3)                                                       as P (Bm) = a (1-a) m-1

        =1 –  a(1 –a)1-1 – a (1-a)2-1– a (1-a)3-1                          

        = (1-a) 3

        = 0.57

(b)

Probability of billed for nine minutes or less= P (nine minutes or less)

                                                                            = ∑i=19 a (1-a)i-1

                                                                      = 1 – (0.57)3