# Thread: X~Exp(x,θ) prove or disprove that E[x^2]=2 (θ)^2

1. ## X~Exp(x,θ) prove or disprove that E[x^2]=2 (θ)^2

X~Exp(x,θ) prove or disprove that E[x^2]=2 (θ)^2.

I know the pdf and how to find E[x^2] but not sure how to show it equals (θ)^2.

2. Originally Posted by nikie1o2
X~Exp(x,θ) prove or disprove that E[x^2]=2 (θ)^2 NOOOO!!!! I think you were trying to write 2 (θ)^-2.

I know the pdf and how to find E[x^2] but not sure how to show it equals (θ)^2.
For an exponential distribution, $E[X^2]=2{\theta}^{-2}=\dfrac{2}{\theta^2}$

$E[X^2]= \displaystyle \int_0^{\infty} x^2\; \theta\;e^{-\theta{x}}\;dx$

integrate by parts..

3. Ah Ha! well i was asked to prove or disprove this so i presume the claim is false then ! I'll have to do an counter example