A store sells X appliances a day, where , and Y extended warranties for those appliances, thus .
The joint p.m.f of X and Y is given as

f (x, y) = c (x + 1) (5 - x) (y + 1) (4 - y)

where x = 0,..., 4 and y = 0,...,3, with .

(a) Find c.

(b) Sketch the support of X and Y?
I can do this.

(c) Find the marginal p.m.f.’s of X and Y?

(d) Are X and Y independent?

(e) How would you find

(f) Determine the correlation coefficient p?

This is just knowing basic definitions and doing the spadework. For example,

(a) Use the fact that 1 = f(0, 0) + f(1, 0) + f(1, 1) + ..... + f(4, 0) + f(4, 1) + f(4, 2) + f(4, 3).

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