mont4e_sm_ch05_sec06

Therefore a 2 b3 b w1 2 e b ln y 2 if y that

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Unformatted text preview: f X ( y 2 )2 y = 2 ye− y x ≥ 0 . Thus, f Y ( y ) = f X (e y )e y = e y e − e = e y − e y ∞ 5-72 a) Now, ∞ 2 −bv ∫ av e dv must equal one. Let u = bv, then 1 = 0 b) If , then v= f W ( w) = f V for 5-73 If 5-74 ∞ du = a u 2 e −u du. b b3 ∫ 0 b3 a 2a Γ(3) = 3 . Therefore, a = 2 b3 b w1 / 2 e −b ln y ≤ 2 . If y = That is, fY ( y ) = ( x − 2) 2 , then x = 2 − y fY ( y ) = f X ( 2 − y ) | − 1 y 2 = 2− y 16 y = ( 1 )y 4 −1 / 2 + 1 y for The sum of for −1 / 2 0≤ x≤2 and x = 2+ y | + f X (2 + y ) | 1 y 2 −1 / 2 fo...
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