# Thread: Show this is a valid pdf

1. ## Show this is a valid pdf

Show that

fY(y) = 1/(y^2), y >= 1

is a valid pdf but that Y does not have a finite expected value.

2. We know that valid $pdfs$ integrate to $1.$

$\int_1^{\infty} \frac{1}{y^2}dy = \frac{-1}{y}|_{1}^{\infty} = 1$

$E[Y]= \int_1^{\infty} y\times \frac{1}{y^2}dy = \int_1^{\infty} \frac{1}{y}dy= \ln(y)|_{1}^{\infty} = \infty$

Let me know if you have questions.
Anonymous