Project assignment: the aim of this project is to derive and implement a computer algorithm to generate observed values (random samples) of three different random variables using the inverse transform method. the three random variables of interest are: (1) x1~uniform(θ1,θ2), (2) x2~exponential(β), and (3) x3~cauchy(θ). we have not introduced the cauchy random variable in this class but its probability density function (pdf) is given by: ) = (1/pi)(1/(1+(x-theta)^2)) on -[infinity] < x < [infinity], -[infinity] < θ < [infinity].the first part of your assignment is to derive the above procedure for the three random variables x1, x2 and x3.the second part of your assignment is to implement the method in r and provide the following results: 1. generate a random sample of size 100,000 from a uniform(-2,1). 2. generate a random sample of size 100,000 from an exponential(3). 3. generate a random sample of size 100,000 from a cauchy(2).for cases (1) and (2), report the mean and variance of your random sample, and display its histogram. compare the mean, variance and histogram obtained using your approach to those obtained via a random sample using the built-in r functions runif(1,-2,1) and rexp(1,1/3). for case (3), report the median of your random sample and compare it to the median obtained via a random sample using the built-in r function rcauchy(1,2).