Math 481/581 Mathematical Statistics I Fall, 2007
Meetings: TR 10:50-12:05, Engr 187
Instructor: Greg Morrow
Office: EN 271, (719) 262.3184, gmorrow@uccs.edu
Hours: TR 10:15-10:45, TR: 1:45 -2:30.
Video Archive: http://cmes.uccs.edu/Fall2006/Math481/
Prerequisite: Math 381 (a first course in probability and statistics with calculus).
Text: Mathematical Statistics and Data Analysis, 3rd ed., by John A. Rice.
ISBN: 0-534-39942-8
Description. Random Variables, Joint Distributions, Mean, Variance, Covariance, Conditional expectations and conditional distributions, Moment generating function technique, Approximate means and variances, Limit Theorems, Chi-square, t, and F distributions and their derivation from an independent normal sample. Illustration of several important concepts in statistics through a study of survey sampling: finite population correction, confidence intervals and application of the central limit theorem, bias, standard error, mean squared error, experimental design and sampling methods, comparisons of estimators via relative efficiency. Chapters 2 through 7 of the text.
Homework and Tests.
Homework will be due weekly. Late homework will not be accepted. One homework
may be dropped. Students will need to be able write simple programs to
solve computing problems and use software to make graphical displays. MatLab
and Maple are suggested and will be demonstrated in lectures. Please see the following
instructions file to access MatLab from the RATS (remote access terminal
server) using only your UFP account: http://it.eas.uccs.edu/help_sheets/RATS.pdf
The final grade will be based on: homework, 25%, mid-term exams, 25% each, and final exam 25%. All tests are in class.
Grading. 90 = A, 80 = B, 70 = C.
Final Exam: Tuesday, Dec. 11,
Notes 1 Chap.2 examples Notes 2 Notes 3 Notes 4 Notes 5 MATLAB Simulation
Notes 6 Notes 7 Chap 3 Examples pt 2 Notes 8 Notes 9 Notes 10 Notes 11 Notes 12 Notes 13
Notes 17 Notes 18 Notes 19 Notes 20
Test 1 (Chps
2&3): Sept 27; Test 2 (Chps 4&5): Nov. 8;
Final Exam (Chps 6&7): Dec. 11.
HW I. Due: Aug. 30.
Chapter 2: 12, 15, 22, 26, 45, 67.
HW II. Due: Sept. 11.
Chapter 3: 8, 16, 17, 19, 24, 29.
[Hint on 3.24: Given: f_[P](p) = 1, 0<p<1, and f_[X|P](x|p) = p^x(1-p)^(1-x), x=0,1, then one wants to find: f_[P|X](p|0), 0<p<1, and f_[P|X](p|1), 0<p<1.]
HW III. Due: Sept. 13.
Chapter 3: 32, 33, 35.
HW IV. Due: Sept. 20.
Chapter 3: 37, 40 (Grad), 45, 49, 66 (Grad), 67, 72.
Test 1: Chapters 2 and 3: Sept.
27.
HW V. Due: Oct. 4.
Chapter 4: 2, 4, 20(Grad), 32, 34.
HW VI. Due: Oct. 16. (NOTE CHANGE of DUE DATE)
Chapter 4: 40, 42, 49, 52, 61, 66, 72.
HW VII. Due: Oct. 23.
Chapter 4: 75, 79, 81, 85, 89, 94(E.C.), 100, 102.
HW VIII. Due: Nov. 1.
Chapter 5: 4, 6(E.C.), 15 (correction: change from 50 to 200
independent fair games), 17, 19,
20(Grad), 22 (See ans. to 21(b) for a=0, b=1, and g=1; also change .05 to .95).
Test 2: Chapters 4 and 5: Nov.
8.
SAMPLE SOLUTION
Review for Test 2
HW IX. Due: Nov. 15.
Chapter 6: 4, 6, 8, 9(Grad; assume an
independent N(0, sigma^2) sample) . Chapter
7: 1, 4.
HW X. Due: Nov. 27.
Chapter 7: 7, 14, 19, 23, 32.
HW XI. Due: Nov. 29.
Chapter 7: 35, 41, 43, 44(Grad), 49 (answer in
book to 7.49 is actually the answer to 7.48.)
The last part of the answer to 7.41(d) in the book is true
under the extra assumption that Var(A)=Var(B). Here A = audited value and B =
book value.
7.49(a): s_R = .0035. For 7.49(d) we have, by 7.44 with
s_x/X-bar in place of C_x, and similarly for C_y, and with rho-hat in place of
rho, that Var(Y-bar_R)/Var(Y-bar)=.56 (approximately).
HW XII. Due: Dec. 6.
Chapter 7: 52, 53, 54(Grad), 55, 57(E.C.), 60.
Final Exam Chapters 6 and 7: Dec.
11, 10:50-1:20.
Dec 11, 2007: Due to weather, the Final Exam has been rescheduled to be a
take home exam, due Dec. 13.