Let's say that we toss 3 fair coins all independently of each other. It turns out that the first coin comes up as Heads. Let us defineY as the number of Heads in tossing the three coins(including the first one)

a)What is the conditional distribution of the number of heads for the remaining two tosses, which is denoted byX, given that the first coin comes up as Heads?

b)Note thatY=X+ 1. What are the expected value and variance ofY?