Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am doing a problem with PDF's and this integral is a roadblock.

I have $f(x)=\dfrac{200}{(x+10)^3}$ where $x>0$ and have solved that $\mathbb{E}(X)=10$.

I am working on finding $\mathbb{E}(X^2)$ and so far have $\mathbb{E}(X^2)=\displaystyle \int_0^\infty \frac{200x^2}{(x+10)^3}$.

How do I go about showing that $\mathbb{E}(X^2)$ diverges? I tried substitution but it doesn't seem to work

share|improve this question
1  
Note that $\frac{x^2}{(x+10)^3}\sim \frac{1}{x}$ –  Pedro Tamaroff Mar 19 '12 at 22:20

2 Answers 2

Comparison to $\int_1^{\infty}x^{-1}\,dx$.

share|improve this answer

Using partial fractions $$\int \frac{200 x^2}{(x+10)^3} dx = \frac{4000}{x+10} - \frac{10000}{(x+10)^2} +200 \, \log_e(x+10)+c$$

and $\log_e(x+10)$ increases without limit as $x$ increases.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.