Expected Value of Rolls of a Dice

Question

Roll a single die. Let X represent the number of rolls needed to get a 3 and let Y represent the number of rolls to get a 4. Find the following:

a)E(X)

b) E(X|Y=1)

c) E(X|Y=5)

Answer 1

1(1/6) + 2(1/6) + 3(1/6) + 4(1/6) + 5(1/6) + 6(1/6)

 

(1/6) ( 1 + 2 + 3 + 4 + 5 + 6)

(1/6)(21)

 

21/6 = 7/2 = 3 and 1/2