Let a, b, c, d be any numbers with a < b and c < d. Let k be a constant, and let X and Y be jointly continuous with joint probability density function
In other words, f (x, y) is constant on the rectangle a < x < b and c
a. Show that 
.
b. Show that the marginal density of X is 
=1 /(b–a) for a < x < b.
c. Show that the marginal density of Y is 
=1 /(d–c) for c
d. Use parts (a), (b), and (c) to show that X and Y are independent.
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