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tutprac4 - 620-202 Practice Class/Computing Laboratory 4...

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620-202 Practice Class/Computing Lab- oratory 4. 1. (6.8-1) Let X be the length of a male grackle (a type of bird). Suppose X N ( μ, 4 . 84). Find the sample size that is needed if we are to be 95% confident the maximum error (ie. z α/ 2 ( σ/ n )) of the estimate of μ is 0.4. ( z 0 . 025 = 1 . 96) 2. (6.8-7) For a public opinion poll for a close election, let p denote the proportion of votes who favour candidate A. How large a sample should be taken if we want the maximum error of the estimate of p to be equal to (a) 0.03 with 95% confidence? (b) 0.02 with 95% confidence? (c) 0.03 with 90% confidence? ( z 0 . 05 = 1 . 645). 3. (6.9-3) Let Y 1 < · · · < Y 5 be the order statistics of 5 independent observations from an exponential distribution that has a mean of θ = 3. (a) Find the p.d.f. of the sample median Y 3 . (b) Compute the probability that Y 4 < 5. (c) Determine P (1 < Y 1 ). 4. (6.9-9) Let X 1 , . . . , X 10 be a random sample of size n = 10 from a distribution with p.d.f. f ( x ; θ ) = exp( - ( x - θ )), θ x < . (a) Show that Y 1 = min( X i ) is the maximum likelihood estimator of θ .
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