Check when x is an exponential rv with pdf

Assignment Help Basic Statistics

Reference no: EM13144975

Let X be a continuous random variable, with CDF F(x), taking values in an interval [0, b]; that is, F(0) = 0 and

F(b) = 1. Then there is an alternative formula for expected value:

E(X) = Z b0 (1 - F(x)) dx. (1)

(a) Assume b is a finite number. Prove (1) using integration-by-parts. [Hint: Recall that the PDF is f(x) = d
dxF(x).]

(b) Check that the formula (1) holds when X Unif(0, b).

Reference no: EM13144975

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