Question

A graduating student keeps applying for jobs until she has three offers. The

probability of getting an offer at any trial is 0.48.

a. What is the expected number of applications? What is the variance?

Answer 1

It is a negative binomial distribution: $X\sim NB(s, p).$

Given $s=3, p=0.48.$

a)

$$E(X)=s/p$$

$$=3/0.48=6.25$$

$$Var(X)=s(1-p)/p^2$$

$$=3(1-0.48)/(0.48)^2=6.770833$$