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1. Let X be a random variable with cumulative distribution function FX , and let Y = X + b, Z = aX, and W = aX + b, where a and b are any constants. Find the cumulative distribution functions FY , FZ , and FW . Hint : The cases a > 0, a = 0, and a <>0 require different arguments.

2. Let X be a random variable with density function fX , and let Y = X + b, Z = aX, and W = aX + b, where a /= 0. Find the density functions fY , fZ , and fW.

2. Let X be a random variable uniformly distributed over [c, d], and let Y = aX + b. For what choice of a and b is Y uniformly distributed over [0, 1]?

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