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StatORJune05 - 2 p 0.5 0.5 and Y 2 4 p 0.3 0.7 Find the...

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Part B: Probability Question for Common Qualifying Exam June 2005 1. A hat contains 3 chips numbered 1, 2, and 3. Two chips are drawn successively from the hat without replacement. What is the correlation between the number on the first chip and the number on the second chip? 2. Consider two independent discrete random variables X and Y the Probability Mass Functions (PMFs) are defined by the following tables: X 1
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Unformatted text preview: 2 p 0.5 0.5 and Y 2 4 p 0.3 0.7 Find the Moment Generating Function of Z=Y X . 3. Let X and Y be independent exponential random variables with the expectations 1/ ± and 1/ μ respectively. Find the Probability Density Function (PDF) of Z=X+Y. 4. Let X have a binomial distribution with parameters n and p , and let the conditional distribution of Y given x X = be Poisson with mean x . What is the variance of Y ?...
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