Question

a probability density function pdf is f(x)=1/(x^2) 1 12 years ago

Answer 1

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

Answer 2

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

Answer 3

It's Ok.

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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.