hw7 - 1. Suppose that Y have the pdf: fY (y ) = (a) Show...

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1. Suppose that Y have the pdf: f Y ( y ) = ( 2( θ - y ) θ 2 , 0 < y < θ 0 , otherwise (a) Show that Y θ is a pivotal quantity. (b) Find the cdf of Y θ . (c) Use (a) to find a 90% confidence interval for θ . 2. Suppose that the random variable Y has a Gamma distribution with parameters α = 2 and an unknown λ . (a) Show that 2 λY has a χ 2 distribution with 4 degrees of freedom. (b) Use (a) to derive a 95% confidence interval for λ . [Hint: Lecture Notes, Ch1-6, p.80, item 6 and p.83, item 2.]
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This note was uploaded on 03/11/2011 for the course STA 506 taught by Professor Lisa during the Spring '11 term at West Chester.

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