Derive equation (5.7). That is, prove that if \(0\[
E|y-X|=2 y F(y)-y+\frac{\alpha}{\alpha+\beta}-2 \frac{B(\alpha+1, \beta)}{B(\alpha, \beta)} G(y),
\]
where \(G\) is the \(\operatorname{CDF}\) of \(\operatorname{Beta}(\alpha+1, \beta)\).

Transcribed Image Text:

E|X X'| = 2e-2 [Io (2X) + I1(2X)].