Use a linear congruential generator with parameters a = 5, c = 9, m = 128 and Z0 = 71 to generate a series of 30 numbers uniformly distributed in the interval [0,1].

a) Compute and compare the mean and variance of these numbers with those obtained from the expected theoretical Uniform(0,1) distribution (continuous uniform). Explain any differences.

b) The interest rate for a capital project is unknown. An accountant has estimated that the minimum interest rate will be between 2% and 5% within the next year. The accountant believes that any interest rate in this range is equally likely. Using the uniform random numbers from part a) generate 30 independent interest rate values for this situation.