Use the Rejection Method to generate n = 10000 values for a random variable X that has the pdf of f(x) = (x^2)/9, 0<x<3. Create a density histogram for your generated values. Superimpose the probability density function of the target distribution to the histogram. Use the generated values to estimate the mean, standard deviation, and the probability that X < 2.

Use the Rejection Method to generate n = 10000 values for a random variable X that has the pdf of f(x) = (x^2)/9, 0<x<3. Create a density histogram for your generated values. Superimpose the probability density function of the target distribution to the histogram. Use the generated values to estimate the mean, standard deviation, and the probability that X < 2.

Two mechanics are changing oil filters for the arriving customers. The service time has an Exponential distribution with mean 12 minutes for the first mechanic, and mean 3 minutes for the second mechanic. When you arrive to have your oil filter changed, your probability of being served by the faster mechanic is 0.8.