Suppose you want to collect a set of 5 distinct baseball car

Suppose you want to collect a set of 5 (distinct) baseball cards. Assume that you buy one card at a time, and each time you get a randomly chosen card (from the 5 different cards available). Let X be the number of cards you have to buy before you collect all the 5. Describe X as a sum of geometric random variables. Find E(X) and Var(X)

Solution

Sol)

Let X follows geometric random variable

n=5 and p=1/5

Mean= (1/p) =5

variance= (1-p) / p²   =( 4/5) / ( 1/25)

variance = 20