# plot the logistic p.d.f.

x = seq(0,1,0.0001)
#x

y = log(x/(1-x))
#y

X11()
par(mfrow=c(2,2))
plot(x,y,type='l',main="transformation")

F_y = exp(y)/(1+exp(y))
#F_y

plot(y,F_y,type='l',main="cdf")

f_y = exp(y)/(1+exp(y))^2
#f_y

plot(y,f_y,type='l',main="pdf")

mu = 1
sigma = .5
f_y = (1/sigma)*exp((y-mu)/sigma)/(1+exp((y-mu)/sigma))^2
f_y

plot(y,f_y,type='l',main="pdf, mu = 1, sigma=0.5")