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Unformatted text preview: 4 . On a given morning an investor is going to buy shares of whichever stock is less expensive. (10) (a) Find the density function for the price per share of whichever stock is less expensive. (10) (b) Find the expected cost per share that the investor will pay. 2 (20) 4. The number of breakdowns per week for a type of PC is a random variable Y -Po( 8 ). A random sample Y t (t = 1, 2, . .., T) of observations on the weekly number of breakdowns is available. The weekly cost of repairing these breakdowns is C = 3Y +Y 2 . Find E(C) and provide an unbiased estimator of it. 5. Consider a random sample Y t (t = 1, 2, . .., T) from a distribution with p.d.f.: where r > 0 is known and 2 is unknown. (5) (a) Find the distribution of . (5) (b) Find the maximum likelihood estimator of 2 . (5) (c) Is an unbiased estimator of 2 ? (5) (d) Does achieve the Cramer-Rao lower bound in finite samples?...
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- Fall '10