What is the expected value of 1/(1+X) with X ~ Beta(2,3)?
2026-04-09 04:25:34.1775708734
Expected Value of Beta Distribution
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The PDF of $X$ is $12x(1-x)^2$. You have to compute $$ 12\int_0^1 \frac1{1+x}x(1-x)^2dx = 12\int_0^1\left(4-3x+x^2-\frac4{1+x}\right)dx = 34 - 48 \log(2) . $$