Question: If I am given two discrete random variables X and Y along with their joint pmf as the following: P = [ X = i

If I am given two discrete random variables X and Y along with their joint pmf as the following:

P=[X=i,Y=j]=(1i/i!)(2j/j!)exp(1+2)

can I assume they are independent since they are clearly the multiplication of two Poisson random variables?

If not, how can I derive the marginal distribution for X?

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