Unformatted text preview: six numbers. De±ne two random variables X and Y as: X ( ω ) = b 1 ω is odd ω is even Y ( ω ) = b ω is odd 1 ω is even Are X and Y independent? Provide clear arguments to support your answer. Problem 4. [15 pt] Let X be a random variable that has a socalled Laplacian distribution, i.e., its pdf is given by f X ( x ) = 1 2 λ e1 λ  x  ,∞ < x < ∞ where λ is a deterministic parameter 1 . Let X 1 ,...,X N be independent random variables with the same exponential distribution as X . You can imagine these as observations of X that you have not collected yet. Design an unbiased estimator of λ that uses X 1 ,...,X N . 1 This distribution is important in image and speech analysis Prabir Barooah 1...
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 Fall '08
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 Probability theory, unbiased estimator, Prabir Barooah, Aerospace Engineering Instructor, following proposed estimator

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