I have two questions.

1. I am given the probability distributions for X and Y (picture above), and I have to find the probability distribution for Z = XY. Do I simply multiply the probabilities of X and Y or do I need to find their pdfs first? (Also, this was just the distribution of a fair coin being tossed.

2. For the second question (the picture above), I am given a joint PDF for X and Y and I am asked to find their marginal PDFs. I've done for X, and I'd like to know if I've done it right. If yes, then I can continue with Y myself.

Thanks in advance. (click on pictures to see full questions)

I have two questions.

1. I am given the probability distributions for X and Y (last picture below), and I have to find the probability distribution for Z = XY. Do I simply multiply the probabilities of X and Y or do I need to find their pdfs first? (Also, this was just the distribution of a fair coin being tossed.

2. For the second question (the picture above), I am given a joint PDF for X and Y and I am asked to find their marginal PDFs. I've done for X, and I'd like to know if I've done it right. If yes, then I can continue with Y myself.

Thanks in advance. (click on pictures to see full questions)

Table for the joint distribution of X and Y