Pr[X = 1] = 0.25
Pr[X = 2] = 0.15
Pr[X = 3] = 0.05
Pr[X = 9] = 0.55

Problem #2 - In class you learned about the inversion method to generate random variables from various distributions. The program here generates and plots a histogram for exponentially distributed random variables. Change the program to generate unif(1.0, 10.0) (i.e., uniformly distributed continuous-valued random variables between 1.0 and 10.0). Submit the program and an output from an execution.

Problem #3 - You are give the following population data:

1, 2, 1, 4, 5, 1, 3, 3

Problem #4 - Being able to characterize measurement data is very important as a first step to building a workload model for a simulation. A data set of 1 million values is found here. You are to find the population mean and variance, plot the histogram, and plot the autocorrelation for up to 100 lags. The tools on the Christensen tools page may be useful (hint: look at summary1.c, hist.c, and autoc.c).

Problem #5 - Being able to generate empirically distributed random variables is a very powerful "trick". Write your own C program or use the existing genemp.c on the Christensen tools page to generate empirically distributed random variables that match the data set from problem #2. Using your program generate 1 million values in a file. This is a "synthetic" data set. Now, repeat problem #2 (i.e., find the mean, variance, histogram, and autocorrelation) for the synthetic data set. Explain any differences in the characterization results for the actual and synthetic data sets.