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A stick of length 2 is broken into two pieces at a uniformly random chose point. What is the expected value of the largest piece?

Here is what I have

$U(X) = 2-x$ if $0\leq x \leq 1$

$U(X) = x$ if $0\leq x \leq 1$

But how do I proceed to find the expected value?

user59036
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1 Answers1

5

Let $Y$ be the length of the largest stick and $X$ be the distance from the left end where the stick is broken. $Y=2-X$ if $0\le X\le 1$ and $Y=X$ else. We need to find $E(Y)$.

$$E(Y)=\int_0^1 \frac{2-x}{2}dx+\int_1^2 \frac{x}{2}dx$$

Sasha
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Bravo
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