If a random variable X has the PDF f(x) = 1/2; -1 < x < 1, then the PDF of Y = X 2 is:
Explanation
F Y(y) = P(Y ≤ y)
⇒ P(X 2≤ y)
⇒ P(X ≤ √y)
⇒ FX(√y) = \(\smallint \nolimits_o^{ - \;\surd y}\) 1/2dy
⇒ ½(y) o-√ y
⇒ ½(1/√y
∴ The PDF of Y = X 2IS (1/2√y)
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