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20105ee131A_1_ps5_2010fall

# 20105ee131A_1_ps5_2010fall - Characteristic function of...

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EE 131A Problem Set 5 Probability Wednesday, November 3, 2010 Instructor: Lara Dolecek Due: Wednesday, November 10, 2010 Reading: Chapter 4 of Probability, Statistics, and Random Processes by A. Leon-Garcia 100 points total 1. Conditional probability refresher. Problem 4.173, page 231 of ALG 2. Function of rv refresher. Let X be exponentially distributed with parameter λ . Let Y be the integer-valued random variable defined in terms of X such that Y = m if m X < m + 1, where m is non-negative integer. Find pmf of Y . What is the name of this random variable ? 3. Markov inequality. Problem 4.97, parts (a), (b) and (d) only, page 224 of ALG 4. Characteristic function of exponential rv. Problem 4.104, page 224 of ALG 5. Characteristic function of uniform discrete rv.
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Unformatted text preview: Characteristic function of uniform discrete rv. Let X be uniform on { 1 , 2 ,...,m } . Find characteristic function of X . 6. Sum of uniform discrete rvs. Let X and Y be independent, uniform discrete random variables, taking values in the set { 1 , 2 ,...,m } . Let Z = X + Y . Compute pgf and pmf of Z . 7. Chernoﬀ bound for exponential rv. Problem 4.108, page 225 of ALG 8. Pgf of geometric rv. Problem 4.109. page 225 of ALG 9. Pgf of binomial rv. Use probability generating function to compute mean and variance of X ∼ Binomial ( n,p ). 10. Poisson bounds. Let X be Poisson with parameter λ . Show that P ( X ≥ 2 λ ) ≤ 1 λ . 1...
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• Fall '10
• Dolecek
• Probability theory, Lara Dolecek, Characteristic function, EE 131A Probability, Conditional probability refresher

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