Math 3215

Grading

The course will be taught in the first half by Professor Spruill and in the second by Mr. Hua Xu. Your grade in the course will be determined from four seventy minute tests, a homework/in-class grade as

course grade = (G_S + G_X)/2

where

G_S = 0.90*(T1+T2)/2 + 0.10*HWIC_S

G_X = 0.90*(T3+T4)/2+ 0.10*HWIC_X.

The fourth exam will be given during the final examination period.

Annotated assignments from our course text Probability and Statistical Inference, 6th ed., by Hogg and Tanis.
Due dates.
Simulation example 2.1-1 of Hogg and Tanis. The correct probability of at least one match in tossing a fair die 6 times is 0.665. You can simulate 50 observations of this experiment. By copying down in the spread sheet you can simulate as many as you like.
Sample first exam .
Sample second exam .
Standard probability distributions
Reproductive properties and linear combinations
Relative frequency histograms and continuous random variables

If you have a Java capable browser you can utilize this section.

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.

If you have release 4 of Maple V or later on your machine you can utilize this section.

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.