Question: Let (X) and (Y) be jointly distributed discrete random variables. Their joint probability distribution is given in the following table: (a) Calculate the marginal probability

Let $X$ and $Y$ be jointly distributed discrete random variables. Their joint probability distribution is given in the following table:

X Y 1 2 3 4 5 f(x) 1 .02 .04 .06

(a) Calculate the marginal probability distribution of $X$.
(b) Calculate the marginal probability distribution of $Y$.
(c) Are $X$ and $Y$ independent random variables? Explain why or why not.
(d) Calculate the conditional probability $P(X=3 Y=1)$.

X Y 1 2 3 4 5 f(x) 1 .02 .04 .06 .08 .05 2 .08 .02 .10 .02 .03 3 .05 .05 .03 .02 .10 4 .10 .04 .05 .03 .03 f(y)

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