W3600_Quiz2_Sol

W3600_Quiz2_Sol - SIEO 3600(IEOR Majors Solution of Quiz 2...

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Unformatted text preview: SIEO 3600 (IEOR Majors) Solution of Quiz 2 Introduction to Probability and Statistics April 21, 2010 Page 1 of 5 Quiz 2 Place all answers on the question sheet provided. This quiz is open textbook (Ross) and open notes/homework. You are allowed to use a calculator, but not a computer. Write all answers clearly and in complete sentences. All answers should be supported by analysis or an argument. This quiz has a total of 25 points. First Name: Last Name: 1 2 Total Honor Code I resolve i ) not to give or receive aid during this examination, and ii ) to take an active part in seeing that other students uphold this Honor Code. Signature: 2 SIEO 3600, Solution of Quiz 2 1. (15 points) Suppose that X ∼ N ( μ 1 ,σ 2 1 ) and Y ∼ N ( μ 2 ,σ 2 2 ) are two independent normal random variables. Tom (a nerd) is interested in computing the PDF of an ugly random variable Z ≡ 1 | 2 X- 3 Y | , with μ 1 = 10, μ 2 = 5, σ 2 1 = 9 and σ 2 2 = 4. However, this looks hard , so Tom decides to proceed in multiple steps : (a) (3 points) If we let U ≡ 2 X- 3 Y (note that Z = 1 / | U | ), what is E ( U ) and Var( U )? Hint : Write U = 2 X + (- 3) Y . Solution: Linearity of expectation implies that E [ U ] = E [2 X- 3 Y ] = 2 E [ X ]- 3 E [ Y ] = 2 μ 1- 3 μ 2 = 5 ....
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W3600_Quiz2_Sol - SIEO 3600(IEOR Majors Solution of Quiz 2...

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