The question is regarding a given pair (X,Y) where x = 0,1,2... and y = x,x+1,x+2,... that have joint PMF of
Px,y(x,y) = (y ; x)*(e^-1)/((2^y)(y!))
I need to utilize this given equation to get marginal PMF of X and Y, and then for conditional PMF od y-x given X = x.
At first I realized that it has similarity toward poisson distribution so I try to relate to poisson. However the lambda values seems to be incorrect. because normally for poisson distribution the general formula is:
P=(e^-lambda)*(lambda^y)/(y!)
however from the above equation the two lamda are not the same. And another problem I'm not sure how to include the matrix column in the calculation.
Thanks for helping.