# Mathematics and Statistics

## Courses - STAT Upper Division

#### 380. Probability and Statistics (3)

Prerequisite: MATH 224.
Frequency interpretation of probability. Axioms of probability theory. Discrete probability and combinatorics. Random variables. Distribution and density functions. Moment generating functions and moments. Sampling theory and limit theorems.
Letter grade only (A-F). Same course as MATH 380. Not open for credit to students with credit in MATH 380. (Lecture 3 hrs.)

#### 381. Mathematical Statistics (3)

Prerequisites: MATH 247, and MATH 380 or STAT 380.
Estimation and hypothesis testing. Maximum likelihood and method of moments estimation. Efficiency, unbiasedness, and asymptotic distribution of estimators. Neyman-Pearson Lemma. Goodness-of-fit tests. Correlation and regression. Experimental design and analysis of variance. Nonparametric methods.
Letter grade only (A-F). (Lecture 3 hrs.) Not open for credit to students with credit in MATH 381.

#### 410./510. Regression Analysis (3)

Prerequisite: STAT 381. (Undergraduates register in STAT 410; graduates enroll in STAT 510.)
Simple linear regression: estimation and inference, prediction, analysis of residuals, detection of outliers, use of transformations. Multiple linear regression: influence diagnostics, multi-collinearity, selection of variables, simultaneous estimation and inference, validation techniques. Statistical software for data analysis used.
Letter grade only (A-F). (Lecture 3 hrs.) Not open for credit to students with credit in MATH 480 or 590.

#### 450./550. Multivariate Statistical Analysis (3)

Prerequisite: STAT 381; Prerequisite/Corequisite STAT 410. (Undergraduates register in STAT 450; graduates enroll in STAT 550.)
Discriminate analysis, principal components, factor analysis, cluster analysis, logistic regression, canonical correlation, multidimensional scaling, and some nonlinear techniques. Statistical software used.
Letter grade only (A-F). (Lecture 3 hrs.) Not open for credit to students with credit in MATH 483 or 593.

#### 475. Data Analysis with SAS (3)

Prerequisite: STAT 381 or consent of instructor.
Topics include: Statistical analysis including extraction, presentation of data in graphical form, creation, modification of datasets, interpretation of output, writing of reports. Provides SAS programming techniques for aforementioned topics preparation for SAS base certification.
Letter grade only (A-F). (Lecture 3 hrs.) Not open for credit to students with credit in MATH 489.

#### 482. Random Processes (3)

Prerequisites: MATH 247, and MATH 380 or STAT 380.
Further topics in probability. Markov processes. Renewal theory. Random walks. Queueing theory. Poisson processes. Brownian motion.
Letter grade only (A-F). (Lecture 3 hrs.) Not open for credit to students with credit in MATH 382.

#### 484. Actuarial Science: Models (3)

Prerequisite: STAT 381 or consent of instructor.
Statistical techniques applied to risk management. Expected utility theory, individual risk models, compound Poisson distributions and processes, ruin probability and first surplus, stop-loss and proportional reinsurance, statistical survival distributions and life tables, life annuity, actuarial present values, and premiums determination.
Letter grade only (A-F). (Lecture 3 hrs.) Not open for credit to students with credit in MATH 484.

#### 485. Actuarial Science: Financial Mathematics (3)

Prerequisite: STAT 381.
Simple and compound interests, stochastic approaches to interest and annuities, stochastic models of stock, Black-Scholes arbitrage pricing of options and other derivative securities, Markowitz portfolio optimization theory, Ito financial calculus, filtrations and martingales.
Letter grade only (A-F). (Lecture 3 hrs.)

#### 495./595. Topics in Modern Statistics (3)

Prerequisite: Consent of instructor. (Undergraduates register in STAT 495; graduates enroll in STAT 595.)
Topics of current interest from statistics literature.
Letter grade only (A-F). Course may be repeated to a maximum of 6 units with different topics. (Lecture 3 hrs)

#### 497. Directed Studies (1-3)

Prerequisite: Consent of instructor.
Junior or senior standing and consent of instructor. Not open to graduate students.