Math 4260 - Introduction to Mathematical Statistics

Office hours for summer 1998: Monday, 8-9 AM, Weds. 11-12 AM, or by appointment

Exam results for the first two exams.

The final exam will be held on Tuesday, September 1 from 8:00-10:50 AM at our usual meeting place.

Grading: There will be two one hour exams worth 100 points each and a final exam worth one or two hundred points, whichever gives the higher course average.

Examinations : All students except video students are expected to take the examinations at the scheduled times. Video students must have their examination solutions FAXed to me at 404-894-4409 in a timely manner to be detailed at the appropriate time. Exams will occur roughly at three week intervals.

Problem assignments : It is recommended that the student work at least the problems on the following list. Problems will not be taken up or graded but some exam questions may consist of exactly these problems or minor variations. The list of problems will not be covered in the order below; the current list for which the student is responsible will be updated from time to time as new material is covered. I look forward to answering questions, including those involving the problem assignments, in class. Questions from off-campus students can be communicated to me by e-mail at spruill@math.gatech.edu or by telephone at 404-894-2718.

Annotated Problems :

Chapter  		 Page	Problems
	1		11	1 - 9 - general baby decision theory
	2		45	11 - minimize mse at mean
	2		50	52 - 55 - computation of Bayes estimators
	2		45	11 - 1, 3 - unbiased estimation
 				4 , 9- unbiased linear estimators and optimal coefficients
 				5 - bias of the minimax proportion estimator
 				6 - mse of minimax estimator
				8 - mvue of Poisson mean
				13 - crlb inappropriate
				14, 15 - mvue for sigma with m known for normal
				17, 19, 22, 23, 28* - computation of mle's
	2		51	39, 40, 42, 45, 47 - confidence intervals
	2		51	60 - prediction
	3		103	1, 2, 3 - computation of a and b 
				5, 9, 10, 11, 14, 15, 22 - most powerful tests
				27, 32, 33 - UMP tests
				38, 42 - SPRT
				45, 46, 50, 52, 57 - lrts
				69, 70 - multiple decision problems
	4		134	2, 4, 6, 8, 9, 10 - least squares and prediction
	3		103	58, 60, 62 - tests of fit
				66 - contingency tables
	

Important Background from Probability

• A sample first exam from the past.
• A sample second exam .
• There are written solutions to problems 9, 10, 27, 33, 52-57, and 69, pg 103.
• The spreadsheet, including formulas, for our sample proportion estimation example is available here if you have a spreadsheet program that reads (I think most do) SYLK files.
• Plotting likelihood functions for i.i.d. samples from a Bernoulli distribution. After you select n, the sample size, and p, the success probability the applet simulates a sample of the required size and plots the log likelihood function upon clicking the mouse while in the window.
• An interactive spreadsheet which simulates exponential data and executes the SPRT for testing the mean is available. You can enter the null and alternative means and the true mean under which the data will be simulated. The nominal types one and two error probabilities can also be entered by the user. After loading, starting with the last row, "FILL DOWN" all the rows to, say, row 300, enter the null and alternative, enter the actual, and watch it work. Scrolling down the page until the first entry in the decision column occurs will tell you the sample size and the decision. All you need is a spreadsheet that will read SYLK files and understand the formulas. The current one was created in Excel 5.0. You can also analyze your own data by replacing the first column with your data.

OTHER LINKS RELATED TO PROBABILITY AND STATISTICS

• Looking up F distribution cutoffs.
• normal lookups, p-values, power functions, simulations, and more
• simulations, table lookups, power functions
• Virtual Laboratory in Probability and Statistics
• influential persons in the development of classical statistics and a biography of the founder of statistical decision theory.