(Challenge exercise) Geno (the women’s basketball coach for UConn) goes to the g

Question

(Challenge exercise) Geno (the women’s basketball coach for UConn) goes to the grocery store and finds that Wheaties is placing pictures of UConn women’s basketball players inside its cereal boxes. A total of 6 players are featured, each appearing with equal probability. Find the expected number of boxes Geno needs to buy in order to obtain pictures of 3 different players. Hint: let X be the total number of cereal boxes that Geno buys and let Ni be the number of boxes that Geno buys to get the ith player after obtaining the i 1th player. Then, X = N1 + N2 + N3. What type of random variable is each Ni? You’ll also need to use the fact that the expected value is linear.

please answer step by step.... thank you so much.

Explanation / Answer

Solution:

Let, X be the no. of boxes that Geno needs to buy in order to obtain pictures of three different players.

Thus X=N1 + N2 + N3

where N2 be the no. of boxes that Geno needs to buy to get second different picture after obtaining the the first

and N3 be the no. of boxes that Geno needs to buy to get third different picture after obtaining the the second.

Clearly N2 follows geometric distribution with success prob.=5/6

and N3 follows geometric distribution with success probability 4/6

Thus E(X)= 1+ E(N2) + E(N3)

= 1+ 6/5 + 6/4

= 3.7

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