Let X 1 , X 2 , and X 3 be three independent Geo(p) distributed random variables, and let Z = X 1 + X 2 + X 3 . a. Show for k ≥ 3 that the probability mass function pZ of Z is given by b. Use the fact...

Let X₁, X₂, and X₃
be three independent Geo(p) distributed random variables, and let Z = X₁
+ X₂
+ X₃.

a. Show for k ≥ 3 that the probability mass function pZ of Z is given by

b. Use the fact that

c. Use E[X1]=1/p and part b to conclude that