Question

A fair coin is to be tossed 3 times. The player receives 10 dollars if all three turn up heads and pays 3 dollars if there is one or no heads. No gain or loss is incurred otherwise. If Y is the gain of the player, what the expected value of Y?

Can anyone provide me the full solutions of this problem.Thanks.

Answer 1

Let X be the number of heads that occurs .

So X~ Bin( 3 , 0.5)

So, P[X=2] = 1- P[X=0]-P[X=1] -P[X=3] = 1- 0.625 = 0.375

Let Y be the gain .

Then Y = 0 if X = 2

= 10 if X = 3

= - 3 if X= 0 or 1

So,