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Let X be a random variable with density function f(x) = 2 5 x for x...

Let X be a random variable with density function f(x) = 2 5 x for x ∈ [2, 3] and f(x) = 0, otherwise. (a) (6 pts) Compute E[(X − 2)3 ] without attempting to find the density function of Y = (X − 2)3 . (b) (6 pts) Find the density function of Y = (X − 2)3

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Answer #1

a) The expected value of (X - 2)3 is computed here using the given density function as:

therefore 0.28 is the required expected value for X here.

b) The Cumulative density function for Y is obtained first here as:

Differentiating this to get the required density function here as:

This is the required PDF for Y here.

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