Given inter arrival mean from an exponential distribution is: 1/lambda = 2.4 The service times should be sampled from a probability density function that has the form: (Cx³, if 0 ≤ x ≤ 2.5 min lo, ifx<0 orx > 2.5 min Question: fx(x)= = How do you use the method of inversion to normalize the constate C that makes fx (x) a proper density function?

Use R to complete the following. R code and R output are requested for solution. Please keep your solution clear and easy to read. Unclear solution will not be grade. O for manual solution. Carry out a simulation experiment to illustrate the central limit theorem when the population distribution is arcsine with probability density function f(x) = 1 T√x(1-x) x = (0, 1). Consider the four sample sizes n = 1, n = 3, n = 5, n = 10, and in each case use 10,000 replications. Note: To simulate a random sample of size n from the arcsine distribution in R, use the command rbeta(n,1/2,1/2).