The random variable $x$ has normal distribution $N(10,1)$. Find $p(x\mid (x-10)^2 < 4)$.
I have been trying it for hours. I tried to solve $\mathbb{E}[(x-10)^2]$ using $\mathbb{E}[ay + b]$ but I'm not sure if it works for $x^2$.
Maybe with the $\mathbb{E}$ and $\mathbb{V}ar$ I can plug into another formula for conditional Gaussians.
This plot may help you see the appropriate integral: