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Suppose that X is a random variable with pdf f(x) = cxe^(-x) for 0<x<1 and 0...

Suppose that X is a random variable with pdf f(x) = cxe^(-x) for 0<x<1 and 0 elsewhere.

a. find the value of c

b. find the expectation of x

c. find the variance of x

Math   Statistics-And-Probability   
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Answer #1

a) since f(x) is a pdf integrating over its ranges equals 1.

(Integrating by parts )...........(i)

b)

....from (i)

                    .........................(ii)

c)

....................(from (ii) )

Thus,

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