Let X and Y be two independent random variables, and g : R2 --> R an...

Let X and Y be two independent random variables, and g : R2 --> R an arbitrary bivariate function.

1) Suppose that X and Y are continuous with densities fX and fY . Prove that for any y ? R withfY (y) > 0, the conditional density of the random variable Z = g(X, Y ) given Y = y is the same as the density of the random variable W = g(X, y).

2) Suppose that X and Y are discrete with probability mass functions pX and pY . Prove that for anyy ? R with pY (y) > 0, the conditional probability mass function of the random variable Z = g(X, Y ) given Y = y is the same as the probability mass function of the random variable W = g(X, y).

Thanks a lot!

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orchestra answered 1 year ago

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