Test_2_2006 - 4 . On a given morning an investor is going...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Department of Economics Professor Dale J. Poirier University of California, Irvine December 5, 2006 FINAL EXAM ECON 220A Statistics and Econometrics I (open book) Directions : You must answer each of the following questions. Points (out of 100) are allocated as noted to the left of each question. Allocate your time according to these points. To receive any partial credit, you must show your work. (20) 1. Consider a random sample Y t (t = 1, 2, . .., T) from a N( : , F 2 ) distribution with unknown mean and variance. Also consider the following loss function for estimating F 2 : Finally, consider estimators of the form for some constant d, where S 2 is the usual unbiased estimator of F 2 . Find the value of d which minimizes risk. (20) 2. Consider a random sample Y t (t = 1, 2, . .., T) from the gamma distribution G( " , $ ). Find a method of moments estimator of " and $ . 3. Suppose the opening prices per share X 1 and X 2 of two similar stocks are independent random variables with common density f X (x) = ½ exp[-½(x-4)], 4 < x <
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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 &gt; 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?...
View Full Document

Page1 / 2

Test_2_2006 - 4 . On a given morning an investor is going...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online