6. Suppose that we are interested in the probability a vacuum salesman makes his

Question

6. Suppose that we are interested in the probability a vacuum salesman makes his first sale on the Yth house call. Suppose the probability of a success is .2 on any one trial, that is, it follows a Geo(.2).

(a) Find the probability he or she makes the first sale on the 5th house call.

(b) What is the expected value and variance of the number of house calls?

(c) Suppose that we were interested in when we have three successful sales, not just the first one. What distribution would this be? What is the expected value of the distribution?

Now I have calculated parts a and b and am confident with my answers for these but I have a question with part c. I believe it is a negative binomial distribution and that the answer would be .008 which I calculated by multiplying the probability of .2 times 3 for the third sale, am I correct in this line of thinking? Or would I have to refer back to my work for parts a and b? Any help would be appreciated thanks!

Explanation / Answer

a)probability he or she makes the first sale on the 5th house call =(1-0.2)4*0.2=0.08192

b)expected value =1/0.2=5

and vcariance=(1-p)/p2 =(1-0.2)/(0.2)2 =20

c) this one is negative binomial distribution

and expected value of this =r/p =3/0.2=15 ; as r represent the number of houses till process ends

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