sample3 - Sample Problems Statstics 517 1. This problem...

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Unformatted text preview: Sample Problems Statstics 517 1. This problem consists of a collection of unrelated short questions. (a) Let X 1 , , X n be a random sample from Poisson( ). Show that n i =1 X i is dis- tributed as Poisson( n ). (Hint: The moment generating function of Poisson( ) is M ( t ) = e ( e t- 1) .) (b) f ( x ; ) = 1- 2 ( x- 1 2 ), 0 < x < 1 and- 1 < < 1. Which of the following is the UMP critical region of size for testing H : = 0 vs H 1 : 6 = 0? The sample size n is 1. i) { x } ii) { x 1- } iii) { x 1- 2 or x 2 } iv) UMP does not exist. 2. Let X 1 , , X n be a random sample from distribution with the following probability density function. f ( x ; , 2 ) = 1 x 2 2 e- (ln x- ) 2 / 2 2 , x >- < < , > 0. (ln in the above pdf is the natural log function.) This distribution is called a lognormal distribution....
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This note was uploaded on 09/10/2009 for the course STATS 517 taught by Professor Song during the Fall '07 term at Purdue University-West Lafayette.

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sample3 - Sample Problems Statstics 517 1. This problem...

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