Syllabus and homework problems for Math 481

Syllabus and homework problems for Math 481 (Spring 2009)


Textbook: John E. Freund's Mathematical Statistics with Applications, Seventh Edition, by Miller and Miller, Pearson/Prentice-Hall (ISBN 0-13-142706-7).

Session
Date
Section Topics Homework Exercises Date due
#1
1/20
4.2-5 Distribution functions and expectations of random variables, Chebyshev inequality, moments, moment-generating functions Ch. 4: 74 1/27
6.2-4 Uniform r.v., Gamma r.v, Chi-square r.v., Beta r.v. Ch. 6: 51, 53, 54, 59 1/27
#2
1/22
4.6-7 Joint and Marginal Distributions,
Linear combinations of r.v., Covariance
Ch. 4: 50, 78 1/27
6.5 Normal r.v. Ch. 6: 63, 65
Typo: In #63 (b) and (d) reverse the inequalities
1/27
7.5 Moment-generating function technique Ch. 7: 48 1/27
#3
1/27
8.1-2 Sampling mean, sample variance, normal population,
law of large numbers, central limit theorem
Ch. 8: 64, 68, 69, 70, 72 2/03
#4
1/29
8.4-5 Sample variance, chi-square, t-statistic, Ch. 8: 24, 26, 75, 76, 77 2/03
#5
2/03
8.6 F-distribution and variance ratio statistic Ch. 8: 39, 40, 42, 80, 81 2/10
#6
2/05
8.7 Order statistics Ch. 8: 47, 48, 86, 87
Typo: In #87 the reference should be to Exercise 8.47
2/10
8.3 Sampling without replacement from finite population Ch. 8: 65 2/10
#7
2/10
10.1-2 Point Estimation: mean-square error, bias, consistency Ch. 10: 3, 13, 14, 15, 17 2/17
#8
2/12
10.3-4 Point Estimation: Cramer-Rao lower bound, mean vs. median, efficiency Ch. 10: 25, 30, 33, 35, 36 2/17
#9
2/17
10.7-8 Maximum Likelihood Estimators; moment estimation Ch. 10: 54, 59, 60, 61, 62 2/24
#10
2/19
10.5 Sufficient statistics Ch. 10: 42, 43, 45, 46, 47 2/24
#11
2/24
11.1-3 Confidence intervals for means Ch. 11: 1, 24, 28, 30, 36 3/03
#12
2/26
First midterm exam (closed book -- no confidence intervals)
#13
3/03
6.6 Normal approximation to binomial r.v. Ch. 6: 77 3/10
11.4-7 Confidence intervals for proportions, variances, and ratios of variances Ch. 11: 38, 50, 53, 59 3/10
#14
3/05
12.1-2 Hypothesis testing methodology, level of significance and errors, Type II errors, power function Ch. 12: 3, 6, 7, 8, 37 3/10
#15
3/10
12.4 Neyman-Pearson lemma, likelihood ratio Ch. 12: 11, 12, 13, 14, 15 3/24
#16
3/12
10.5-6 Power function; tests of composite hypotheses, likelihood ratio tests, uniformly most powerful tests Ch. 12: 21, 22, 24, 40, 44
Typos: #22 and #24 refer to Example 10.18; #44 refers to Exercise 12.21
3/24
Spring break
#17
3/24
13.1-3 P-value, one-sided and two-sided alternatives on a scalar parameter,
tests on differences of means
Ch. 13: 25, 30, 31, 36, 40 3/31
#18
3/26
13.4 Hypothesis testing of variances Ch. 13: 6, 7, 47, 51, 54 3/31
#19
3/31
13.5-6 Hypothesis testing of proportions Ch. 13: 57, 58, 64, 66, 67 4/07
#20
4/02
13.7-8 Contingency tables, chi-square statistics, Goodness of Fit Ch. 13: 14, 68, 74, 77, 78 4/07
#21
4/07
13.8 Goodness of Fit Ch. 13: 80, 81 4/16
3.7 Conditional Probability Ch. 3: 105, 107 4/16
4.8 Conditional Expectation Ch. 4: 82 4/16
#22
4/09
10.9 Bayesian estimation; binomial populations with prior beta, normal populations Ch. 10: 77, 93, 94, 96, 97 4/21
#23
4/14
Second midterm exam (closed book -- no Bayesian estimation)
#24
4/16
14.1-3 Regression curves, linear prediction, least-squares curve fitting Ch. 14: 1, 7, 8, 42, 43 4/21
#25
4/21
6.7 Bivariate normal distribution Ch. 6: 46, 47 4/28
14.4 Normal regression analysis Ch. 14: 51, 53, 54 4/28
#26
4/23
14.4 Sampling distribution of regression coefficients Ch. 14: 28, 69 4/30
#27
4/28
14.5 Normal correlation analysis; distribution of sample correlation coefficient Ch. 14: 31, 65, 66 4/30
#28
4/30
Catch up and review
5/13 8:00 - 11:00 am (room TBA)   Final exam (open book and notes)

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Prof. Roe Goodman   (goodman at math dot rutgers dot edu) / Revised June 4, 2009