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Question 3 Suppose the random variable X has the uniform distribution, fX(x) = 1, 0 <...

Question 3 Suppose the random variable X has the uniform distribution, fX(x) = 1, 0 < x < 1. Suppose the random variable Y is related to X via Y = (-ln(1 - X))^1/3.

(a) Demonstrate that the pdf of Y is fY (y) = 3y^2 e^-y^3, y>0. (Hint: Work out FY (y))

(b) Determine E[Y ]. (Hint: Use Wolfram Alpha to undertake the integration.)

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