Question

The pdf of X is f(x) = 2xe−x2, 0 < x < ∞ and zero otherwise....

The pdf of X is f(x) = 2xe−x2, 0 < x < ∞ and zero otherwise. Find the pdf of W = X2.

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Answer #1

The CDF for X here is obtained as:

Let n = k2, then dn = 2k dk

Therefore, we get here:

Now using this CDF, the CDF for W here is obtained as:

Therefore the PDF for W here is obtained as:

This is the required PDF for W here.

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