Question: Consider a box that has five white marbles and two yellow marbles. A marble is drawn out and not replaced, and then a second marble

Consider a box that has five white marbles and two yellow marbles. A marble is drawn out and not replaced, and then a second marble is chosen. Random variable X is 1 if the first marble is yellow and 0 otherwise. Random variable Y is 1 if the second marble is yellow and is 0 otherwise.

(a) What is the joint probability distribution of X and Y?

(b) Find the correlation coefficient.

(c) Are X and Y independent? Explain.

(d) Find Var(X + Y).

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