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-2yfor x> 0 and y> 0. a.(15 points) What is the probability that 0 < y < 1? b.(10 points)Are Xand Yindependent? 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 ABCXXX, are calculated. a.(10 points) What is an unbiased point estimate of the thickness of the
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