Use Rstudio when asked to. This is both about probability statistics and Rstudio coding. Please screenshot the Rstudio codes, outputs, graphs. Please show all your workings and answers for the calculation questions too.

3) Inversion sampler for a discrete random variable A discrete random variable X has the probability mass function x 1 2 3 4 5 f(x) 0.1 0.2 0.4 0.1 0.2 a) Write R code for an inversion sampler to generate a sample of 1000 random numbers from the distribution of X. Use the generated CNRG pseudo-random numbers of Question 1 (do not use any functions, which directly implement the sampler like rbinomO) b) Show the probability mass function of the sample of simulated random numbers. Include the true probability mass function in the plot for a comparison