Suppose Peter receives 3 “wrong number” phone calls on his cell phone each week

Question

Suppose Peter receives 3 “wrong number” phone calls on his cell phone each week on average. Assume the number of “wrong number” phone calls that Peter receives on his cell phone each week has a Poisson distribution. Answer the following questions. For full marks, relevant R code and output must be included.

a) What’s the probability that Peter will not receive any “wrong number” phone calls next week?

b) What’s the probability that Peter will receive exactly 5 “wrong number” phone calls in the next two weeks?

c) What’s the probability that Peter will receive 3 or more “wrong number” phone calls in the next two weeks?

Can you show me how to use R lab to do this question? Thank you

Explanation / Answer

> #lambda =average number of wrong phone call in each week
> lambda<-3
> # Part a) Peter not receive any wrong number phone in next week
> ppois(0,lambda)
[1] 0.04978707
> # part b) Average number of wrong phone calls for two weeks =2*3=6
> Lambda2<-6
> #Peter will not receive exactly 5 wrong number phone calls,in then next two weeks .
> #P(x =5)
> x1<-4
> x2<-5
> ppois(x2,Lambda2)-ppois(x1,Lambda2)
[1] 0.1606231
> #Part c) Peter will receive 3 or more wrong number .
> #P(x >=3) = 1 - P(x <=2)
> 1-ppois(2,Lambda2)
[1] 0.9380312
>

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