Suppose Y has density function f(y) 3 2 y 2 , 1 y 1 Find the density function for (a) U 3Y , (b) V 3 Y , (c) W Y 2 Ans (a) f U (u) u 2 18, 3 u 3 (b) f V (v) (3 2)(3 u) 2 , 2 v 4 (c) f W (w) (3 2)w, 0 w 1

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Question: Suppose Y has density function f(y) = 3/2 y 2 , 1 < y < 1. Find the density function for (a) U = 3Y

Suppose Y has density function f(y) = 3/2 y², 1 < y < 1. Find the density function for (a) U = 3Y , (b) V = 3 Y , (c) W = Y². Ans. (a) f_U(u) = u²/18, 3 < u < 3 (b) f_V (v) = (3/2)(3 u)², 2 v 4 (c) f_W (w) = (3/2)w, 0 w 1

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