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HW9_Problem_Set - W is the error W and S are independent...

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ORIE 3500/5500 Fall Term 2008 Assignment 9 Note that the due date is Monday, November 17 , at 1:00 pm you need to mention your section number on the top of your answer script. 1. [5 + 5 = 10 pts] In the month of September the probability of rainfall in Ithaca in any day is 0 . 25 independent of other days. If it rains in some day, then the amount of rainfall has an exponential distribution with parameter 1 / 2. Find the (a) mean and (b) variance of total rainfall in Ithaca in September. 2. [10 pts] A signal S has exp(1) distribution. It is recorded after it has passed through one filter. The filter adds an independent random error which has Uniform (0 , 1) distribution. So the recorded signal is Y = S + W , where
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Unformatted text preview: W is the error. W and S are independent. Find the least square estimate of S given the value y of Y . 3. [10 pts] A weighing machine always overestimates the weight of a person by an amount that is uniformly distributed between 0 and 5 lb. Assume that the weight distribution of people in a community is uniform between 100 and 200 lb. Find the linear least square estimate of the weight of a person based on the reading of the weighing machine. 4. [5 + 10 = 15 pts] Suppose X and Y have joint PDF f X,Y ( x, y ) = 25 e-5 y , ≤ x ≤ y < ∞ . Find (a) the least square estimate of X based on Y and (b) linear least square estimate of X based on Y . 1...
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