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Let X ~ Uniform [0, 1] and Y = X n . (a) Find the CDF of Y. (b) Find the pdf of Y. (c)

Let X ~ Uniform [0, 1] and Y = Xⁿ.

(a) Find the CDF of Y.

(b) Find the pdf of Y.

(c) Find E[Y].

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Question

Let X ~ Uniform [0, 1] and Y = X n . (a) Find the CDF of Y. (b) Find the pdf of Y. (c)