Question

Assume that Y_(1),Y_(2),dots,Y_(n) is a sample of size n from an exponential distribution with mean \theta . (a) Use the method of moment-generating functions to show that 2\sum_(i=1)^n (Y_(i))/(\theta ) is a pivotal quantity and has a \chi ^(2) distribution with 2n df. (b) Use the pivotal quantity 2\sum_(i=1)^n (Y_(i))/(\theta ) to derive a 95% confidence interval for \theta . (c) If a sample of size n=7 yields /bar (y)=4.77, use the result from part (b) to give a 95% confidence interval for \theta .

          Assume that Y_(1),Y_(2),dots,Y_(n) is a sample of size n from an exponential distribution with mean \theta .
(a) Use the method of moment-generating functions to show that 2\sum_(i=1)^n (Y_(i))/(\theta ) is a pivotal quantity and has a \chi ^(2) distribution with 2n df.
(b) Use the pivotal quantity 2\sum_(i=1)^n (Y_(i))/(\theta ) to derive a 95% confidence interval for \theta .
(c) If a sample of size n=7 yields /bar (y)=4.77, use the result from part (b) to give a 95% confidence interval for \theta .

assume that y1y2dotsyn is a sample of size n from an exponential distribution with mean theta a use the method of moment generating functions to show that 2sumi1n yitheta is a pivotal q 40935

Added by Reginald L.

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