3.5 The pdf of a logistic random variable with parameter > 0 is f(x) = ex (1 + ex) 2 , for x >

3.5 The pdf of a logistic random variable with parameter λ > 0 is f(x) = λe−λx

(1 + e−λx)

2 , for x > 0

a) Calculate the cdf of the distribution.

b) Calculate the inverse cdf F−1.

c) Write a code to generate random numbers with the logistic distribution.

d) Calculate the expectation EX =

 ∞

0 xf(x)dx and the variance