Question: A random variable X has the probability-density function where α is an arbitrary positive constant. (a) Determine the characteristic function M x (jv). (b) Use

A random variable X has the probability-density function

-ах {3 аеах, х > 0 Sx (х) %— 0, х <0

where α is an arbitrary positive constant.
(a) Determine the characteristic function Mx(jv).

(b) Use the characteristic function to determine E[X] and E[X2].

(c) Compute σ2x.

- {3 , > 0 Sx () % 0,

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