quiz-09-24

quiz-09-24 - terval on the real line between and . Then f X...

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M4056 Quiz 5, Sept. 24, 2010 Name 1. Recall that the Poisson distribution is a discrete distribution with pmf f ( x | λ ) = e - λ · λ x x ! , x = 0 , 1 , 2 , . . . a. Let v X = ( X 1 , . . ., X n ) be a sample from a Poisson distribution. Write the sample pmf explicitly as a function of vx = ( x 1 , . . ., x n ): f v X ( vx | λ ) = b. Show that n i =1 X i is a suFcient statistic for λ . 2. Suppose that X 1 , . . ., X n are independent and uniformly distributed on the open in-
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Unformatted text preview: terval on the real line between and . Then f X i ( x i | ( , )) = b 1 - , if < x i < ; , otherwise. Show that T ( v X ) = (min { X 1 , . . ., X n } , max { X 1 , . . ., X n } ) is a suFcient statistic for the vector parameter ( , )....
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