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Solved: Let X have a logistic distribution with pdf f(x) = ex (1 + ex)2 , < x < . Show
Chapter 5, Problem 5.1-6(choose chapter or problem)
QUESTION:
Let X have a logistic distribution with pdf
\(f(x) = \frac {e^{-x}}{(1 + e−x)^2}\),\(\quad -\infty < x < \infty\).
Show that
\(Y = \frac {1}{1 + e^{-X}}\)
has a U(0, 1) distribution.
Questions & Answers
QUESTION:
Let X have a logistic distribution with pdf
\(f(x) = \frac {e^{-x}}{(1 + e−x)^2}\),\(\quad -\infty < x < \infty\).
Show that
\(Y = \frac {1}{1 + e^{-X}}\)
has a U(0, 1) distribution.
ANSWER:Step 1 of 3
Let X be the random variable with PDF,defined over
Now, define,
For the defined range of X, Y lies between 0 and 1.