Question: A random variable X has the pdf f X (x) = Ae -bx [u(x) - u(x - B)] where u(x) is the unit step function

A random variable X has the pdf 

fX(x) = Ae -bx [u(x) - u(x - B)]

where u(x) is the unit step function and A, B, and b are positive constants.

(a) Find the proper relationship between the constants A,b, and B. Express b in terms of A and B.

(b) Determine and plot the cdf.

(c) Compute E(X).

(d) Determine E(X2).

(e) What is the variance of X?

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