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?

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kalsoomtahir1 kalsoomtahir1 · Answer 1 · 2020-09-18T13:05:37+02:00

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

Sam1s Sam1s · Answer 2 · 2022-02-06T19:00:34+01:00

Given:

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)

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

The probability that a call will be billed for nine minutes or less :

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

= ∑i=19 a (1-a)i-1

= 1 – (0.57)3

=0.814

The probability that a call will be billed for nine minutes is less .

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