# Two fair dice are rolled. Let X denote the smallest value of the two dice, and Y denote the product of the two dice. (a) Find fX,Y(x,y), fX(x), and fY(y) [you do not need to determine the mathematical function for these, it is fine to just list the probabilities]. (b) Find prob(X=2|Y=12) and prob(Y=12|X=2). (c) Find E(Y|X=2). (d) Find Cov(X,Y). (e) Find Corr(X,Y).

Question

Two fair dice are rolled. Let X denote the smallest value of the two dice, and Y denote the product of the two dice.

(a) Find fX,Y(x,y), fX(x), and fY(y) [you do not need to determine the mathematical function for these, it is fine to just list the probabilities].

(b) Find prob(X=2|Y=12) and prob(Y=12|X=2).

(c) Find E(Y|X=2). (d) Find Cov(X,Y).

(e) Find Corr(X,Y).

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