The joint probability mass function of X and Y is x = 0, 1, ... , y

Question:

The joint probability mass function of X and Y is

P(X = x,Y = y) = e²y!(x – y)! |

x = 0, 1, ... , y = 0, 1, ... ,x.

(a) Find the conditional distribution of Y given X = x.
(b) Describe the distribution in terms of distributions that you know.
(c) Without doing any calculations, find E[Y|X = x] and V[Y|X = x].

Distribution
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