Let X and Y be jointly continuous with joint probability density function f (x, y) and marginal densities 
and 
. Suppose that f (x, y)=g(x)h(y) where g(x) is a function of x alone, h(y) is a function of y alone, and both g(x) and h(y) are nonnegative.
a. Show that there exists a positive constant c such that 
.
b. Use part (a) to show that X and Y are independent.
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