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Solved: Let X have a logistic distribution with pdf Show
Chapter 5, Problem 6E(choose chapter or problem)
Let \(X\) have a logistic distribution with pdf
\(f(x)=\frac{e^{-x}}{\left(1+e^{-x}\right)^{2}}, \quad-\infty<x<\infty\)/ .
Show that
\(Y=\frac{1}{1+e^{-X}}\)
has a \(U(0,1)\) distribution.
Equation Transcription:
Text Transcription:
X
f(x)=e^-x/(1+e^-x)2^, - infinity <x< infinity
Y=1/1+e^-X
U(0,1)
Questions & Answers
QUESTION:
Let \(X\) have a logistic distribution with pdf
\(f(x)=\frac{e^{-x}}{\left(1+e^{-x}\right)^{2}}, \quad-\infty<x<\infty\)/ .
Show that
\(Y=\frac{1}{1+e^{-X}}\)
has a \(U(0,1)\) distribution.
Equation Transcription:
Text Transcription:
X
f(x)=e^-x/(1+e^-x)2^, - infinity <x< infinity
Y=1/1+e^-X
U(0,1)
ANSWER:
Step 1 of 3
Define a variable Y for the logistically distributed variable X over as,
Thus, Y is defined over .