The random variables X and Y are discreet distributed with the values 1,2,3,4 and 0,1,2,3. Y is B(3, 0.5)-distributed. Given below is the table for the conditional probabilities P(X = i|Y = k) for i = 1,2,3, 4 and k = 0,1,2,3:

Calculate P(X = i, Y = k) for i = 1, . . . , 4 and k = 0, . . . , 3.

I think what is required here is the joint probability.

So that calulates to P(X = i, Y = k)P(Y = k). We already have (X = i, Y = k) in the table already but I don't know how I will get P(Y=K)

Thanks in advance for any help.