A random variable Y has a beta distribution of the second
Chapter 6, Problem 105SE(choose chapter or problem)
A random variable Y has a beta distribution of the second kind, if, for
\(\alpha>0 \text { and } \beta>0\), its density is
\(f_{Y}(y)=\left\{\begin{array}{ll} \frac{y^{\alpha-1}}{B(\alpha, \beta)(1+y)^{\alpha+\beta}}, & y>0 \\
0, & \text { elsewhere } \end{array}\right.\)
Derive the density function of \(U=1 /(1+Y)\)
Equation Transcription:
{
Text Transcription:
\alpha >0 and \beta > 0
fY(y)= {y ^ \alpha-1B(\alpha,\beta )(1+y)^\alpha+\beta, y > 0, 0, elsewhere
U=1/(1+Y)
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