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Could somebody tell my how to calculate $EU(X+2)$, where $U(X)={\sqrt X}$ and X is distributed evenly over the interval $[a,b]$?

batonas su braškėm
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    I assume that you're talking about expected values and probabilities. I would start by figuring out the cdf and pdf of $U(X)$ and $U(X+2)$ – Matti P. Mar 25 '20 at 09:58

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$$EU(X)=E\sqrt {X+2}=\frac 1 {b-a} \int_a^{b} \sqrt {x+2} dx$$ $$=\frac 2 {3(b-a)} (x+2)^{1.5}|_a^{b}=\frac 2 {3(b-a)}[(b+2)^{1.5}-(a+2)^{1.5}]$$.

Kavi Rama Murthy
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