Assume that $d$ is a random variable with pdf $f_d(x)$, is the following true?
$$E\left[\frac{1}{d^2}\bigg|d>1\right]\leq E\left[\frac{1}{d^2}\bigg|d>1 \cap d<2\right]$$
My answer is yes, since by additional condition on the right side of above equation we are deleting large $d$ area therefore, removing small $\frac{1}{d^2}$ area. Thus, the average should increase. Is that right? How can I see a mathematical solution?