(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If X is a random variable with density function: f(x) = [tex]\lambda[/tex]e[tex]^{-x \lambda}[/tex]where X>=0.

2. Relevant equations

Why is the expected value of X, or E[X] = [tex]\frac{1}{\lambda}[/tex]?

3. The attempt at a solution

E[X] = [tex]\int[/tex] x*([tex]\lambda[/tex]e[tex]^{- \lambda}[/tex][tex]^{x}[/tex]) dx, where the integral is from 0 to infinity.

I let u = -[tex]\lambda[/tex]x

du = -[tex]\lambda[/tex] dx

but I can't get the [tex]\frac{1}{\lambda}[/tex] as the answer when I performed the integration.

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# Homework Help: Integral involving exponential logarithm

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