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HW6-2 - ECE 302 Homework#6 Due date 2/23...

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ECE 302, Homework #6. Due date: 2/23 http://www.ece.purdue.edu/ chihw/ECE302 07.html Prof. Chih-Chun Wang Email: [email protected] Office: MSEE354 Office Hours: MWF: 12pm–1pm TA: Kamesh Krishnamurthy, Email: [email protected] Office: POTR 370 Office Hours: M: 10–11am TTh: 10:30am–12:30pm Review of Calculus: Question 1: (Compare it with HW5Q1). Consider a continuous random variable X with the following pdf f X ( x ): f X ( x ) = ( 3 e - 3 x if x [0 , ) 0 otherwise A discrete “quantizer” Y of X is as follows. For any X , if 1 . 5 k X < 1 . 5( k + 1), then Y = k . For example, if the X value is π , then Y = 2 since 1 . 5 × 2 π < 1 . 5 × 3. If the X value is - 1 . 1, then Y = - 1. Find the pmf of the discrete variable Y . Namely, find P ( Y = k ). What type of random variables is Y ? Question 2: What is the sample space of a geometric distribution? Plot the generalized pdf of a geometric distribution with parameters p = 2 / 3. (The range of your horizontal axis should be large enough to cover k = 3.) Question 3: Consider a binomial distribution with parameters p = 1 / 3 and n = 4. What is the sample space? Find the conditional cdf
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