(Solution) - Let X have pdf fx x 2 9 x 1 -(2025 Original AI-Free Solution)

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Let X have pdf fx(x) = 2/9(x + 1), - 1 < x < 2.
(a) Find the pdf of Y = X2. Theorem 2.1.8 is not directly applicable in this problem.
(b) Show that Theorem 2.1.8 remains valid if the sets A0, A1,..., Ak, contain X, and apply the extension to solve part (a) using A0 = ?, A1 = (-2,0), and A2 = (0,2).