Question: Suppose X and Y have joint probability density f(x, y) = g(x)h(y) for some functions g and h which depend only on x and y,

Suppose X and Y have joint probability density f(x, y) = g(x)h(y) for some functions g and h which depend only on x and y, respectively. Show that X and Y are independent with fX(x) ∝ g(x) and fY(y) ∝ h(y).

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