What is $E[||X|-2|]$? Can I just get rid of the $2$ and continue or should I look at two different values, one for greater than $0$ and the other less than $0$?
2026-03-30 00:19:13.1774829953
What is $E[||X|-2|]$? The expected value of an absolute value
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It looks like you need to integrate over 4 intervals. If $f(x)$ is your density function, let $g(x)$ be the function in $E[||X|-2|]=\int g(x)f(x)dx$ over the relevant interval. Then:
Over $(-\infty,-2)$, $g(x)=-x-2$
Over $(-2,0)$, $g(x)=x+2$
Over $(0,2)$, $g(x)=2-x$, and
Over $(2,\infty)$, $g(x)=x-2$