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PSTAT 109: Quiz 1 Winter 2014

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Question;PSTAT 109: Quiz 1Winter 2014Instructions: Please show all work in an organized fashion for full credit.Problem 1.Check if the following functions are density functions:(a)f(x) =x_1[0,1](x)(b)f(x) =x2_1[0,1](x)(c)f(x) =e????x_1[0,1)(x)Problem 2.Compute the cumulative distribution functionFof the following densities:(a)f(x) = 2x_1[0,1](x)(b)f(x) = 3x2_1[0,1](x)(c)f(x) =e????x_1[0,1)(x)Problem 3.Compute the expectationsE[X], whereXis the \random variable" having thefollowing densities:(a)f(x) = 2x_1[0,1](x)(b)f(x) = 3x2_1[0,1](x)

 

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