Question: 27. Let the joint probability density function of two random variables X and Y satisfy where g and h are two functions from R to

27. Let the joint probability density function of two random variables X and Y satisfy

f(x,y) = g(x)h(y), -xx

where g and h are two functions from R to R. Show that X and Y are independent.

f(x,y) = g(x)h(y), -xx

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