2. (L.O. 3.4) A computer help center lassifies all incoming calls into exactly o

Question

2. (L.O. 3.4) A computer help center lassifies all incoming calls into exactly one of two possible categories: calls about "hardware" or calls about "software." Independent of all other calls, suppose an incoming call is about hardware with probability 0.5. the following questions, treat each part separately. (a) Given that the first two calls are about software, what is the expected number of additional calls until the first call about hardware? (b) What is the expected number of calls until the second call about hardware? (e) What is the variance of the expected number of calls until the second call about hardware?

Explanation / Answer

(A)

Let X is a random variable shows the number of calls until the first hardware call. Here X has geometric distribution with parameter p=0.5. So expected number of calls for first hardware call is

E(X) = 1/ p = 1/0.5 = 2

Since geometric distribution is memory less so each time it start as fresh event.

So correct answer is D.

(b)

Here negative binomial distribution with parameters r=2 and p=0.5 will be used.

So expected number of calls is  

r /p = 2 /0.5 = 4

Answer: option E

(c)

The variance is

[ r(1-p)] / p^2 = [2 * (1-0.5) ] / (0.5^2 ) = 4

Answer: option E

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