R project 1

I need 2 files， HTML and RDM files. The description of your project is provided in the following.

• 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<x<1, zero elsewhere
• (b) f(x)=1/x² , 1<x<, zero elsewhere
• 2. Let X have the uniform pdf f(x)=1/π 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. Suppose we wish to generate a sample from the exponential (β) distribution, and only have access to a computer which generates numbers from the skew logistic distribution. It turns out that if X~SkewLogistic (β), then log(1+exp(-X)) is exponential (β). Show that this is true and check by simulation that this transformation is correct.
• 4. n 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 and R code to plot different densities for Y² using the same parameters.