a probability density function pdf is f(x)=1/(x^2) 1

Question

a probability density function pdf is f(x)=1/(x^2)  1<x<∞
find cdf F(x) And what is unusual about this distribution?

anonymous · Answer

$$\large{F(x) = \int\limits_{1}^{x}\frac{1}{x^2}dx}$$

anonymous · Answer

Thanks @exraven 
$$F(x) = 1-x^{-1}$$ is this right?

john_es · Answer

It's Ok.

john_es · Answer

I think it should be interesting to answer the last question that says the problem.

anonymous · Answer

Hi @John_ES 
May I ask what is unusual about this distribution?

john_es · Answer

I would say that the pdf function has no inflection points, but I'm not sure about this.

john_es · Answer

I mean, I'm not sure is this the true reason they ask for.

ybarrap · Answer

Its mean is infinite:

$$
\bar{x}=\int_1^{\infty}xf(x)dx=\int_1^{\infty}x\cfrac{1}{x^2}dx=\int_1^{\infty}\cfrac{1}{x}dx=\ln x|^\infty_1=\infty
$$

I think this is unusual.