Math 3215

Grading

Your grade in the course will be determined from three hour tests, a homework/class grade, and a final exam as

course grade = (2*Exam1 +2*Exam2 + hwcl + 2*Exam3 + 3*finalexam)/10.

Date of exam 3 is

Solution to problem 8.7 of Meyer.

Course Text: Introductory Probability with Statistical Applications by P. Meyer.

Annotated assignments from our course text. Homework will be collected and graded but you may work together on it.
Standard probability distributions
Reproductive properties and linear combinations
Relative frequency histograms and continuous random variables

Select a random sample, without replacement, of your desired sample size from the numbers 1 to a population size you set. After entering the population size and sample size click on the "sample without replacement" button. The program will then select a random sample to your specifications and you can see all the numbers by hitting reload on your browser and scrolling, or you can save them to a file (on the Mac) by putting the cursor in the large white area, selecting all, and copying.
You can "look up" a standard normal probability; just enter the desired z and press the calculate button.
An M/M/1 queue has Poisson arrivals and exponential service times. You can pick arrival and service rates and watch a real-time simulation. Coded by Johnny Tyme (J. Tong).
Simulate sample paths of a Poisson process. Coded by Dale Everett.
You can simulate Weibull random variables and plot the histogram of your simulation and the density on the same axes. Coded by Russ Keldorph.
Plot normal densities . You can see plotted on the same axes a standard normal density in black and a normal density of your choice in blue. Select a standard deviation by clicking along the horizontal line segement at the top; select a mean by clicking along the horizontal axis.

Simply make sure the settings on your web browser under options:helper applications are MIME Type application/Maple and suffixes are mws,ms.

Simulate Weibull random variables and see plots of the histograms of the results.
In class we proved mathematically that the square of a standard normal random variable has a chi-square distribution with one degree of freedom. Empirical evidence of this can be obtained here. Simulate n standard normal random variables, forming a histogram of their squares, and plotting on the same axis the chi-square 1 density. You can try different values of n. For n a thousand or so you'll observe a pretty close correspondence.
Simulate an instance of the central limit theorem.
Plot histograms of data. First put the file containing the data of interest, an ordinary text file named "somedata," in your Maple folder (or directory). The data should be delimited by spaces or EOL's. There are some sample data sets below which you can try, just select the one of interest. You can easily save the file as required from your browser. Similar instructions apply to see a boxplot of your data.