Problem 3.25. The probability of having a cellular phone call dropped in the mid

Question

Problem 3.25. The probability of having a cellular phone call dropped in the mid- dle of a call while driving on the freeway in a "big" city is characterized by following events 1. A = {call is during rush hour) 2. B = {call is not during rush hour) 3. C = {the call is dropped) 4, D = {the call is normal) Rush hour is defined to be 7-9:00AM and 4-6:00 PM. The system is character- ized with Pl Drop during rush hour-P(CIA) = 0.3 Pl Drop during nonrush hour-P(CIB) = 0.1 Since a call is three time more likely to occur in the daytime than at night, a person's time to make a call, T, might be modeled as a random variable with fr(t) = K 0-t-7 (3.42) = K 21 t 24 =0 otherwise where time is measured using a 24-hour clock (i.e., 4:00PM (a) Find K. (b) Find P(A) (c) What is P(C)? (d) What is the P (A and C) = P (An C)? 16).

Explanation / Answer

a) 7K+ 14*3K+3K=1

K=1/52

b)P(A) = 2K+2*3K=8K=8/52

c)P(C)=0.1*46/52+0.3*8/52 =7/52

d)P( A interection C) = 0.3*P(A)=0.3*8/52=2.4/52

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