Prove Theorem 3.8.2. (Either apply Theorem 3.8.4 or first compute the c.d.f. separately for a > 0 and a In Theorem 3.8.4
Linear Function. Suppose that X is a random variable for which the p.d.f. is f and that Y = aX + b (a ‰  0). Then the p.d.f. of Y is

and 0 otherwise.

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1. f(y-b) ) (3.8.1) g(y)- for-oo < у < oo,