1.Write R code to plot each f(x) and F(x). Note you may want to derive F(x) first for each case.

(a)f(x)=3(1-x)², 0

(b) f(x)=1/x² , 1

2.Let X have the uniform pdf f(x)=1/ for . Find the pdf of Y= tan(X). This is the pdf of Cauchy distribution.Write R code to plot Cauchy density in R.

3.In your WS related to Ch 6, you were asked to find the probability density function of U=Y², if Y is Rayleigh density. Write R code to plot different density of Y for different parameters. Write a R code to plot different densities for Y² using the same parameters.