410Hw07 - STAT 410 Homework#7(due Friday October 21 by 3:00...

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STAT 410 Homework #7 Fall 2011 (due Friday, October 21, by 3:00 p.m.) 0. Warm-up: 4.2.3 1. Suppose P ( X n = i ) = 6 3 + + n i n , for i = 1, 2, 3. Find the limiting distribution of X n . 2. Let X n have p.d.f. f n ( x ) = n n x 2 1 1 1 + + , for 0 < x < 1, zero elsewhere. Find the limiting distribution of X n . 3. 4.3.2 Let Y 1 denote the minimum of a random sample of size n from a distribution that has p.d.f. ( ) ( ) θ - - = x e x f , θ < x < , zero elsewhere. Let Z n = n ( Y 1 θ ). Investigate the limiting distribution of Z n . 4. 4.3.3 Let Y n denote the maximum ( the last order statistic ) of a random sample of size n from a distribution of the continuous type that has c.d.f. F ( x ) and p.d.f. f ( x ) = F ' ( x ). Find the limiting distribution of Z n = n ( 1 – F ( Y n ) ).
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5. a) 4.3.9 Let X be ( ) 50 2 χ . Approximate P ( 40 < X < 60 ). Hint: We already know that ( ) ( ) 1 , 0 2 Y N D n n n - . b)
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410Hw07 - STAT 410 Homework#7(due Friday October 21 by 3:00...

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