I was given the pdf $f(x) = 2x^{-2}$ for $1<x<2$ of a continous random variable $X$. I found the cdf to be $F(x) = \int_{1}^{x}2t^{-2}dt=-\frac{2}{x}+2$. However, I feel like my cdf is wrong, because $P(0.5<X<1.7)>1$ if I use the formula $F(1.7)-F(0.5)$.
Can someone help me figure out what I did wrong?
The point $x = -0.5$ is outside of your domain $x\in [1,2]$ therefore there is nothing wrong with your $cdf.$
Note that you have $F(2)-F(1) =1$ so the function $F(x)$ is correct.