A random variable X has density function f(x)=(1/2)e^(-abs(x)). Prove that the moment-generating function of X is Mx(t)=1/(1-t^2)

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A random variable X has density function f(x)=(1/2)e^(-abs(x)). Prove that the moment-generating function of X is Mx(t)=1/(1-t^2)

Answered Same DayDec 20, 2021

Answer To: A random variable X has density function f(x)=(1/2)e^(-abs(x)). Prove that the moment-generating...

Robert answered on Dec 20 2021
115 Votes
F(x)=1/2e^(-abs(x))
F(x) can be rewritten as
F(x)=(1/2)e^(-x) from x=0 to x=∞ (i.e.) for positive numbers
F(x)=(1/2)e^(x) from x=-∞ to x=0 (i.e.) for negative numbers
F(x)=not defined at x=0
M(x)=∫ ( ) ( )
M(x)=∫ ( ) ( ) ( )


+∫ ( ) ( ) ( )



=∫...
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