Two discrete random variables X and Y have the joint probability mass function

_XY(,)={^x-^y(1)^x-y\y!()!, =0,1,...,;=0,1,2,...

0,

Where and p are constants such with >0 and 0

a. The marginal distribution of X and Y

b. The conditional distribution of Y for a given X, and of X for a given Y

c. Pr{X>1}

Hint: For (a) the answer is _X()=(^x)!,=0,1,2,...; _Y()=()\!, =0,1,2,...].

Show your work getting to these solutions. For you might want to use the infinite series expansion for the exponential function:=_i=0 /! for all x. For review the CDF of the binomial distribution.