MATH 3670 Midterm: MATH 3670 GT sol3770 1 Spring10

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15 Feb 2019
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1) in a bowl there are 3 balls numbered form 1 to 3. Let x1 the result of the rst extraction and x2 the result of the second one. Compute: the joint probability mass function p(x1, x2) of x1 and x2. There are six possible outcomes: {(1, 2), (1, 3), (2, 3), (2, 1), (3, 2), (3, 1)} and they have all the same probability. So we have p(1, 2) = p(1, 3) = p(2, 3) = p(2, 1) = p(3, 2) = p(3, 1) = 6 p(1, 1) = p(2, 2) = p(3, 3) = 0: the probability mass function of y = x1 +x2 and the expected value e(x1+x2). There are 3 possible values for y : 3, 4 and 5. Each of them can be obtained in two ways. The expected value is py (3) = py (4) = py (5) =

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