410Hw08 - STAT 410 Homework #8 (due Friday, October 28, by...

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STAT 410 Homework #8 Fall 2011 (due Friday, October 28, by 3:00 p.m.) 1. 4.3.16 Hint: + + + = 1 2 1 2 n n t n t e o n t for large n . 2. 4.3.17 Hint: Use Theorem 4.3.9. 3. Let Y n be χ 2 ( n ). What is the limiting distribution of Z n = n n Y - ? Hint: We already know that ( ) n n n 2 Y - = - 1 Y 2 n n n ( ) 1 , 0 N D . 4. Let X 1 , X 2 , … , X n be a random sample from the distribution with probability density function ( ) ( ) ( ) θ 1 1 θ θ ; X x x f - + = , 0 < x < 1, θ > – 1. Recall: θ ~ = 2 X 1 - is the method of moments estimator of θ . Show that θ ~ is asymptotically normally distributed ( as n ). Find the parameters.
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5. Let X 1 , X 2 , … , X n be a random sample from the distribution with probability density function ( ) ( ) ( ) θ 1 1 θ θ ; X x x f - + = , 0 < x < 1, θ > – 1. a) What is the probability distribution of Y = ( ) = - - n i i 1 X 1 ln ? b)
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410Hw08 - STAT 410 Homework #8 (due Friday, October 28, by...

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