Question: 22. Let X be a continuous random variable whose probability density function f is even; that is, f (x) = f (x), x. Prove that

22. Let X be a continuous random variable whose probability density function f is even; that is, f (−x) = f (x), ∀x. Prove that

(a) the random variables X and −X have the same probability distribution function;

(b) the function MX(t) is an even function.

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