Test_1_2010 - (20) 2. Suppose X -U(0, 1) and Y * X = x...

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Department of Economics Professor Dale J. Poirier University of California, Irvine October 26, 2010 MIDTERM 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. Results from the text need not be reproduced in detail - you can merely cite the source. 1. Urn A contains 2 white balls and 1 black ball. Urn B contains 1 white ball and 5 black balls. A ball is drawn at random from urn A and placed in urn B. Then a ball is drawn at random from urn B. (10) (a) What is the probability that the ball drawn from urn B is white? (10) (b) Are the events “the ball drawn from urn A is white” and “the ball drawn from urn B is white” independent? Explain.
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Unformatted text preview: (20) 2. Suppose X -U(0, 1) and Y * X = x -U(x, 1). Find the marginal p.d.f. of Y. (20) 3. Take a stick of unit length and break it at random. Let X be the break point. Then X -U(0, 1). Let Y be the length of the longer piece. What is the mean of Y? 4. Let the p.d.f. of the random variable Y be f Y (y) = " y- ( " + 1) for y $ 1, and equal to zero otherwise, where " > 0. (6) (a) Find the median of Y. (14) (b) Suppose you have a computer program to generate uniform random variables over [0, 1]. How can you use it to generate draws on the random variable Y? 5. Let X be a random variable with p.d.f. f(x) = c(1 + x)-2 for x > 0, and zero otherwise, where c > 0 is a constant. (5) (a) Find c. (5) (c) Let Y = " + F R n(X). Find its p.d.f. . (5) (b) Find the c.d.f. of X. (5) (d) Find the c.d.f. of Y....
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This note was uploaded on 12/13/2011 for the course ECON 220a taught by Professor Poirier,d during the Fall '08 term at UC Irvine.

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