$X$ is $N(10,1)$. Find $f(x|(x-10)^2 < 4)$
This is a homework question. I can only figure out that X is normally distributed with mean 10 and variance 1.
Can you please explain what is meant to be found here.
Thanks.
2026-05-05 17:42:44.1778002964
Homework Help. Probability Density Functions.
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It is best to rewrite $\{x\;|\;(x-10)^2<4\}$ as $\{x\;|\;-2<x-10<2\}$. In terms of the normalized quantity $z=(x-\mu)/\sigma$ this is $\{z\;|\;-2<z<2\}$.
I don't know what $f$ is doing in this problem. If what you really meant was $P\{x\;|\;(x-10)^2<4\}$, then a table of probabilities for $z$-scores is all you need.