Distribution Function f(x)= .5e^|x|, find EX and Var(x)

[badgerbadger]

Let X be a continuous random variable with density function

f(x)= .5e^|x|

for x range R. Find EX and Var(x)

help please!

 

[HallsofIvy]

Check your problem again. That is NOT a density function. $\int_{-\infty}^\infty f(x)dx$ is not even defined, much less being 1. Did you mean $f(x)= 0.5e^{-|x|}$?

 

[badgerbadger]

haha yeah its f(x)= 0.5e^{-|x|}

sorry about that.

 

[HallsofIvy]

Then $E(x)= \int_{-\infty}^{\infty}xe^{-|x|}dx$ which you should be able to get by "symmetry" without needing to do the integral.

And then $Var(X)= \int_{-\infty}^{\infty}x^2e^{-|x|}dx= 2\int_0^\infty x^2e^{x}dx$ which you can do integrating by parts (twice).