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Let random variable X ∼ U(0, 1). Let Y = a + bX, where a and...

Let random variable X ∼ U(0, 1). Let Y = a + bX, where a and b are constants.

(a) Find the distribution of Y .

(b) Find the mean and variance of Y .

(c) Find a and b so that Y ∼ U(−1, 1).

(d) Explain how to find a function (transformation), r(), so that W = r(X) has an exponential distribution with pdf f(w) = e^ −w, w > 0.

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