11SMT2

# 11SMT2 - Midterm#2 of ECE302 Prof Wang's section 89pm...

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Midterm #2 of ECE302, Prof. Wang’s section 8–9pm Thursday, March 3, 2011, MTHW 210. 1. Please make sure that it is your name printed on the exam booklet. Enter your student ID number, e-mail address, and signature in the space provided on this page, NOW! 2. This is a closed book exam. 3. You have one hour to complete it. The students are suggested not spending too much time on a single question, and working on those that you know how to solve. 4. There are 12 pages in the exam booklet. Use the back of each page for rough work. 5. Neither calculators nor help sheets are allowed. Name: Student ID: E-mail: Signature:

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Question 1: [25%, Work-out question, Outcome 1] 1. [10%] X is a binomial random variable with n = 3 and p = 1 / 3. Find the conditional expectation E ( X | X 1). 2. [15%] X is an exponential random variable with λ = 1. Find the probability P (sin( X · π ) > 0). Hint: when X = 22 . 5, sin( X · π ) = 1, and when X = 9 . 5, sin( X · π ) = - 1.

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Question 2: [10%, Work-out question, Outcome 1] X is a Bernoulli random variable with p = 1 1 . 7 . Construct a new random variable Y = X 1 . 7 ln(1+ X ). Find the variance Var ( Y ).
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## This note was uploaded on 02/12/2012 for the course ECE 302 taught by Professor Gelfand during the Spring '08 term at Purdue.

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11SMT2 - Midterm#2 of ECE302 Prof Wang's section 89pm...

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