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Unformatted text preview: ECE 302, Homework #6, due date: 2/23/2011 http://cobweb.ecn.purdue.edu/ ∼ chihw/11ECE302S/11ECE302S.html Review of Calculus: The chain rule. Question 1: Consider the following functions. F ( x ) = Z x f ( s ) ds g ( x ) = F ( h ( x )) = Z h ( x ) f ( s ) ds Express d dx F ( x ) and d dx g ( x ) using f ( x ) and h ( x ). Question 2: [Intermediate/Exam Level] (Compare it with HW4Q1). Consider a continu ous random variable X with the following pdf f X ( x ): f X ( x ) = 1 . 5 e 3  x  for all x (1) Consider a discrete “quantizer” Y of the magnitude of X as follows. For any X , if k ≤  X  < k + 1, then Y = k . For example, if the X value is π , then Y = 3 since 3 ≤   π  < 4. If the X value is 1 . 25, then Y = 1. Find the pmf of the discrete variable Y . Namely, find P ( Y = k ) for k = 0 , 1 , 2 ··· . What type of random variables is Y ? Question 3: [Intermediate/Exam Level] Let X = Y 1 + Y 2 + ··· + Y n be a binomial random variable that results from the summation of n independent Bernoulli random variables Y 1 to Y n . The success probability of Y i is p for i...
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 Spring '08
 GELFAND
 Probability theory, CDF, Intermediate/Exam Level

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