UC Davis 2008-2010 General Catalog - General Catalog - UC Davis

488 Statistics
Total Units for the Major.................. 82-83
Major Adviser. J. Jiang
Students are encouraged to meet with an adviser to
plan a program as early as possible. Sometime
before or during the first quarter of the junior year,
students planning to major in Statistics should consult
with a faculty adviser to plan the remainder of their
undergraduate programs.
Minor Program Requirements:
The Department offers a minor program in Statistics
that consists of a survey at the upper division level of
the fundamentals of mathematical statistics and of
the most widely used applied statistical methods.
UNITS
Statistics............................................... 20
Statistics 106, 108, and 130A-130B or
131A-131B .........................................16
One course from Statistics 104, 135, 137,
138, 141, 142, 144, 145...................... 4
Preparation. Statistics 13 or 32 or 100 or
102.
Graduate Study. The Graduate Program in Statistics
offers study and research leading to the M.S.
and Ph.D. degrees in Statistics, including a Ph.D. in
Statistics with an emphasis in Biostatistics. Detailed
information concerning these degree programs, as
well as information on admissions and on financial
support, is available from the Department of Statistics.
Graduate Adviser. P. Burman
Statistical Consulting. The Department provides
a consulting service for researchers on campus. For
more information, call the Statistical Laboratory
office (530) 752-6096.
Courses in Statistics (STA)
Lower Division Courses
10. Statistical Thinking (4)
Lecture—3 hours; discussion/laboratory—1 hour.
Prerequisite: two years of high school algebra. Statistics
and probability in daily life. Examines principles
of collecting, presenting and interpreting data
in order to critically assess results reported in the
media; emphasis is on understanding polls, unemployment
rates, health studies; understanding probability,
risk and odds. GE credit: SciEng or SocSci,
Wrt.—III. (III.)
12. Introduction to Discrete Probability (4)
Lecture—3 hours; laboratory—1 hour. Prerequisite:
two years of high school algebra. Random experiments;
countable sample spaces; elementary probability
axioms; counting formulas; conditional
probability; independence; Bayes theorem; expectation;
gambling problems; binomial, hypergeometric,
Poisson, geometric, negative binomial and
multinomial models; limiting distributions; Markov
chains. Applications in the social, biological, and
engineering sciences. Offered in alternate years. GE
credit: SciEng.
13. Elementary Statistics (4)
Lecture—3 hours; discussion—1 hour. Prerequisite:
two years of high school algebra or the equivalent in
college. Descriptive statistics; basic probability concepts;
binomial, normal, Student’s t, and chi-square
distributions. Hypothesis testing and confidence
intervals for one and two means and proportions.
Regression. Not open for credit to students who have
completed course 13V or higher. GE credit: Sci-
Eng.—I, II, III. (I, II, III.)
13V. Elementary Statistics (4)
Lecture—1.5 hours; web virtual lecture—5 hours.
Prerequisite: two years of high school algebra or the
equivalent in college. Descriptive statistics; basic
probability concepts; binomial, normal, Student’s t,
and chi-square distributions. Hypothesis testing and
confidence intervals for one and two means and proportions.
Regression. Not open for credit to students
who have completed course 13 or higher. GE credit:
SciEng.—I. (I.)
32. Basic Statistical Analysis Through
Computers (3)
Lecture—3 hours. Prerequisite: Mathematics 16B or
21B; ability to program in a high-level computer language
such as Pascal. Overview of probability modeling
and statistical inference. Problem solution
through mathematical analysis and computer simulation.
Recommended as alternative to course 13 for
students with some knowledge of calculus and computer
programming. GE credit: SciEng.—II, III. (II,
III.)
90X. Seminar (1-2)
Seminar—1-2 hours. Prerequisite: high school algebra
and consent of instructor. Examination of a special
topic in a small group setting.
98. Directed Group Study (1-5)
Prerequisite: consent of instructor. (P/NP grading
only.)
99. Special Study for Undergraduates (1-5)
Prerequisite: consent of instructor. (P/NP grading
only.)
Upper Division Courses
100. Applied Statistics for Biological
Sciences (4)
Lecture—3 hours; laboratory—2 hours. Prerequisite:
Mathematics 16B or the equivalent. Probability computation/modeling,
estimation, hypothesis testing,
contingency tables, ANOVA, regression; implementation
of statistical methods using computer package.
Only two units credit allowed to students who
have taken course 13 or 32. Not open for credit to
students who have taken course 102. GE credit Sci-
Eng.—I, II, III. (I, II, III.)
102. Introduction to Probability Modeling
and Statistical Inference (4)
Lecture—3 hours; discussion—1 hour. Prerequisite:
two years of high school algebra, and upper division
standing. Introductory probability and statistics
at a rigorous yet precalculus level. Rigorous precalculus
introduction to probability and parametric/
nonparametric statistical inference with computing;
binomial, Poisson, geometric, normal, and sampling
distributions; exploratory data analysis; regression
analysis; ANOVA. Only two units of credit allowed
to students who have taken course 32. Not open for
credit to students who have taken course 100. GE
credit: SciEng.—I, III. (I, III.)
103. Applied Statistics for Business and
Economics (4)
Lecture—3 hours; discussion—1 hour. Prerequisite:
course 13, 32, or 102; and Mathematics 16A, 16B.
Descriptive statistics; probability; random variables;
expectation; binomial, normal, Poisson, other univariate
distributions; joint distributions; sampling distributions,
central limit theorem; properties of
estimators; linear combinations of random variables;
testing and estimation; Minitab computing package.
GE credit: SciEng.—I, II, III. (I, II, III.)
104. Applied Statistical Methods:
Nonparametric Statistics (4)
Lecture—3 hours; laboratory—1 hour. Prerequisite:
course 13, 32, or 102. Sign and Wilcoxon tests,
Walsh averages. Two-sample procedures. Inferences
concerning scale. Kruskal-Wallis test. Measures of
association. Chi square and Kolmogorov-Smirnov
tests. Offered in alternate years. GE credit: Sci-
Eng.—(II.)
106. Applied Statistical Methods: Analysis
of Variance (4)
Lecture—4 hours. Prerequisite: course 13, 32, or
102. One-way and two-way fixed effects analysis of
variance models. Randomized complete and incomplete
block design, Latin squares. Multiple comparisons
procedures. One-way random effects model.
GE credit: SciEng.—I, II. (I, II.)
108. Applied Statistical Methods:
Regression Analysis (4)
Lecture—3 hours; discussion—1 hour. Prerequisite:
course 13, 32 or 102. Simple linear regression,
variable selection techniques, stepwise regression,
analysis of covariance, influence measures, computing
packages. GE credit: SciEng.—I, II, III. (I, II, III.)
120. Probability and Random Variables for
Engineers (4)
Lecture—3 hours; discussion—1 hour. Prerequisite:
Mathematics 21A, B, C, and D. Basic concepts of
probability theory with applications to electrical
engineering, discrete and continuous random variables,
conditional probability, combinatorics, bivariate
distributions, transformation or random
variables, law of large numbers, central limit theorem,
and approximations. No credit for students
who have completed course 131A or Civil and Environmental
Engineering 114. GE credit: SciEng.—I,
III. (I, III.) Mueller
130A. Mathematical Statistics: Brief Course
(4)
Lecture—3 hours; discussion—1 hour. Prerequisite:
Mathematics16B. Basic probability, densities and
distributions, mean, variance, covariance, Chebyshev’s
inequality, some special distributions, sampling
distributions, central limit theorem and law of
large numbers, point estimation, some methods of
estimation, interval estimation, confidence intervals
for certain quantities, computing sample sizes. Only
2 units of credit allowed to students who have taken
course 131A.—I. (I.)
130B. Mathematical Statistics: Brief Course
(4)
Lecture—3 hours; discussion—1 hour. Prerequisite:
course 130A. Transformed random variables, large
sample properties of estimates. Basic ideas of
hypotheses testing, likelihood ratio tests, goodnessof-fit
tests. General linear model, least squares estimates,
Gauss-Markov theorem. Analysis of variance,
F-test. Regression and correlation, multiple regression.
Selected topics.—II. (II.)
131A. Introduction to Probability Theory (4)
Lecture—3 hours; discussion—1 hour. Prerequisite:
Mathematics 21A, B, C, and D. Fundamental concepts
of probability theory, discrete and continuous
random variables, standard distributions, moments
and moment-generating functions, laws of large numbers
and the central limit theorem. Not open for
credit to students who have completed Mathematics
135A.—I, II, III. (I, II, III.) Mueller
131B. Introduction to Mathematical
Statistics (4)
Lecture—3 hours; discussion—1 hour. Prerequisite:
course 131A or Mathematics 135A. Sampling,
methods of estimation, sampling distributions, confidence
intervals, testing hypotheses, linear regression,
analysis of variance, elements of large sample
theory and nonparametric inference.—II, III. (II, III.)
Mueller
131C. Introduction to Mathematical
Statistics (4)
Lecture—3 hours; discussion—1 hour. Prerequisite:
course 131B. Sampling, methods of estimation, sampling
distributions, confidence intervals, testing
hypotheses, linear regression, analysis of variance,
elements of large sample theory and nonparametric
inference.—III. (III.) Mueller
133. Mathematical Statistics for Economists
(4)
Lecture—3 hours; discussion—1 hour. Prerequisite:
course 103 and Mathematics 16B, or the equivalents;
no credit will be given to students majoring in
Statistics. Probability, basic properties; discrete and
continuous random variables (binomial, normal, t,
chi-square); expectation and variance of a random
variable; bivariate random variables (bivariate normal);
sampling distributions; central limit theorem;
estimation, maximum likelihood principle; basics of
hypotheses testing (one-sample).—I. (I.)
135. Multivariate Data Analysis (4)
Lecture—3 hours; discussion—1 hour. Prerequisite:
course 130B, and preferably course 131B. Multivariate
normal distribution; Mahalanobis distance; sampling
distributions of the mean vector and
covariance matrix; Hotelling’s T 2 ; simultaneous inference;
one-way MANOVA; discriminant analysis;
principal components; canonical correlation; factor
analysis. Intensive use of computer analyses and real
data sets.—III. (III.)
Quarter Offered: I=Fall, II=Winter, III=Spring, IV=Summer; 2009-2010 offering in parentheses
General Education (GE) credit: ArtHum=Arts and Humanities; SciEng=Science and Engineering; SocSci=Social Sciences; Div=Social-Cultural Diversity; Wrt=Writing Experience