(a) Let a be a real number such that 1 < a and let X be a random variable corresponding to a real number between 1 and a chosen uniformly at random. Suppose p(15x 1 < X < 8. Determine the value of a. (b) [Let Y = X³. Determine the probability density function of Y.

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A: Pdf of X is f(x)=132(8−x) , 0 ≤ x ≤ 8.

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