Suppose a random variable X has a CDF given by Fx (x) and similarly, a random variable

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Suppose a random variable X has a CDF given by Fx (x) and similarly, a random variable Y has a CDF, Fy (y) . Prove that the function F(x,y) = Fx (x) Fy (y) satisfies all the properties required of joint CDFs and hence will always be a valid joint CDF.
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