PSTAT 109: Quiz 1 Winter 2014

PSTAT 109: Quiz 1 Winter 2014

Question
	
PSTAT 109: Quiz 1















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Winter 2014

Instructions: Please show all work in an organized fashion for full credit.






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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 the
following densities:
(a)f(x) = 2x_1[0;1](x)
(b)f(x) = 3x2_1[0;1](x)