Question: In Example 6.3, we obtained the distribution function of Y = aX + b, when the distribution of X is known and a > 0.

In Example 6.3, we obtained the distribution function of Y = aX +

b, when the distribution of X is known and a > 0. Obtain a similar result for the case when a < 0, i.e. by assuming that the distribution function, F, of the variable X is known, find the distribution function and the density of Y = aX + b.

Application: Find the density function of Y = −4X + 1 for the case where X has density f (x) = 4e−4x, x ≥ 0.

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