Question: Suppose that the random variables (X, Y) have joint probability density function ((x, y). The marginal probability density function of X is defined to be

Suppose that the random variables (X, Y) have joint probability density function ((x, y). The marginal probability density function of X is defined to be

Where ((x) and b(x) are the smallest and largest possible values, respectively, that can be for the given x. Show that
(a)

(b)

.bLx) fx(x) f(x, y) dy P(a < X < b) = | fx(x) dx E (X)xfx(x) dx

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