Quiz2_W06_132C1

Quiz2_W06_132C1 - Department of Chemical Engineering...

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Department of Chemical Engineering University of California, Santa Barbara Ch.E. 132C Winter, 2006 Quiz 2 1. ( 25 points ) The joint probability density function for two random variables is given by f ( x, y ) = 0.5e - x-2y for x > 0 and y > 0. a. (15 points) What is the probability that 0 < y < 1? b. (10 points) Are X and Y independent? Justify your answer. 2. ( 25 points ) A composite material consists of three layers of different materials, A, B and C. The thickness of each layer can be assumed to be normally distributed with a standard deviation of σ =2 mm. Suppose that the thicknesses of ten samples are measured and the sample means for each layer, , , and A BC X XX , are calculated. a. (10 points) What is an unbiased point estimate of the thickness of the
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