Let X~ Bin(100,0.9). For each of the following parts, construct an example showing that it is possible, or explain clearly why it is impossible. In this problem, Y is a random variable on the same...

Let X~ Bin(100,0.9).

For each of the following parts, construct an example showing that it is possible, or explain clearly why it is impossible.

In this problem, Y is a random variable on thesame
probability space
as X; note that X and Y arenot necessarily independent.

(a) Is it possible to have Y~ Pois(0.01) with P(X= Y ) = 1?

(b) Is it possible to have Y~ Bin(100,0.5) with P(X= Y ) = 1?

(c) Is it possible to have Y~ Bin(100,0.5) with P(X= Y ) = 1?