Tutorial 4

Tutorial 4 - THE UNIVERSITY OF HONG KONG DEPARTMENT OF...

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Unformatted text preview: THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT 1302 PROBABILITY AND STATISTICS II (2009-10) EXAMPLE CLASS 4 1. Let X 1 ,X 2 ,...,X n be a random sample from the normal distribution N (0 ,θ ), < θ < ∞ . What is the sufficient statistic for θ . 2. Let X 1 ,X 2 ,...,X n be a random sample from the normal distribution N ( θ,σ 2 ),-∞ < θ < ∞ , where the variance σ 2 is known. Show that ¯ X is a sufficient statistic for the mean θ . 3. Let X 1 ,X 2 ,...,X n denote a random sample from a distribution with p.d.f. f ( x | θ ) = θx θ- 1 , < x < 1 , otherwise , where θ > 0. Use the factorization criterion to show that Q n i =1 X i = X 1 X 2 ··· X n is a sufficient statistic for θ . 4. Let X 1 ,X 2 ,...,X n be a random sample of size n from a geometric distribution. Find the sufficient statistic for θ . 5. If X 1 ,X 2 ,...,X n constitute a random sample from the population given by f ( x ) = e- ( x- δ ) , x > δ , otherwise...
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This note was uploaded on 05/04/2011 for the course STAT 1302 taught by Professor Smslee during the Spring '10 term at HKU.

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Tutorial 4 - THE UNIVERSITY OF HONG KONG DEPARTMENT OF...

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