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# hw8 - STAT 225 Homework 8 Due Monday Do the following...

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STAT 225 - Homework 8 Due Monday 6/22/09 Do the following problems : 1. Page 289, problem 5.138 Hint: The set-up here is: λ Gamma ( α , β ) ( Y | Λ = λ ) P ( λ ) [Λ is upper-case λ ] 2. Let X | Y = y Beta (1 , y ) and Y U (0 , 1) Prove: E ( X ) = ln 2 3. Let ( X, Y ) be jointly continuous with the following joint density: f XY ( x, y ) = 30 y 4 (1 - y ) 2 xe - xy x > 0 0 < y < 1 0 otherwise (a) Find f Y ( y ), the marginal distribution of Y , and identify the distribution you got. (b) Find f X | Y ( x | y ), the conditional distribution of X given Y = y , and identify the distribution you got. (c) Find E ( X ) 4. A bit challenging... Let ( X, Y ) be jointly continuous with the following joint density: f XY ( x, y ) = 1 6 e - x 0 < y < x 3 x > 0 0 otherwise (a) Find f X ( x ), the marginal distribution of X , and identify the distribution you got. (b) Find f Y | X ( y | x ), the conditional distribution of Y given X = x , and identify the distribution you got.

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hw8 - STAT 225 Homework 8 Due Monday Do the following...

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