# Applied Statistics Immersion

## Overview for Applied Statistics Immersion

Deepen your technical background and gain further appreciation for modern mathematical sciences and the use of statistics as an analytical tool.

• This immersion is closed to students majoring in applied statistics and data analytics.
• Students are required to complete at least one course at the 300-level or above as part of the immersion.

The plan code for Applied Statistics Immersion is APSTAT-IM.

## Curriculum Update in Process for 2024-2025 for Applied Statistics Immersion

Current Students: See Curriculum Requirements

Course
Prerequisites
MATH-181
Calculus I (or equivalent)
This is the first in a two-course sequence intended for students majoring in mathematics, science, or engineering. It emphasizes the understanding of concepts, and using them to solve physical problems. The course covers functions, limits, continuity, the derivative, rules of differentiation, applications of the derivative, Riemann sums, definite integrals, and indefinite integrals. (Prerequisites: MATH-111 or (NMTH-220 and NMTH-260 or NMTH-272 or NMTH-275) or equivalent courses with a minimum grade of B-, or a score of at least 60% on the RIT Mathematics Placement Exam. Co-requisites: MATH-181R or equivalent course.) Lecture 6 (Fall, Spring).
MATH-182
Calculus II (or equivalent)
This is the second in a two-course sequence. It emphasizes the understanding of concepts, and using them to solve physical problems. The course covers techniques of integration including integration by parts, partial fractions, improper integrals, applications of integration, representing functions by infinite series, convergence and divergence of series, parametric curves, and polar coordinates. (Prerequisites: C- or better in MATH-181 or MATH-181A or equivalent course. Co-requisites: MATH-182R or equivalent course.) Lecture 6 (Fall, Spring).
Electives
Choose three of the following:*
MATH-251
Probability and Statistics
This course introduces sample spaces and events, axioms of probability, counting techniques, conditional probability and independence, distributions of discrete and continuous random variables, joint distributions (discrete and continuous), the central limit theorem, descriptive statistics, interval estimation, and applications of probability and statistics to real-world problems. A statistical package such as Minitab or R is used for data analysis and statistical applications. (Prerequisites: MATH-173 or MATH-182 or MATH 182A or equivalent course.) Lecture 3, Recitation 1 (Fall, Spring, Summer).
MATH-505
Stochastic Processes
This course explores Poisson processes and Markov chains with an emphasis on applications. Extensive use is made of conditional probability and conditional expectation. Further topics, such as renewal processes, Brownian motion, queuing models and reliability are discussed as time allows. (Prerequisites: (MATH-241 or MATH-241H) and MATH-251 or equivalent courses.) Lecture 3 (Spring).
STAT-205
Applied Statistics�
This course covers basic statistical concepts and techniques including descriptive statistics, probability, inference, and quality control. The statistical package Minitab will be used to reinforce these techniques. The focus of this course is on statistical applications and quality improvement in engineering. This course is intended for engineering programs and has a calculus prerequisite. Note: This course may not be taken for credit if credit is to be earned in STAT-145 or STAT-155 or MATH 252.. (Prerequisite: MATH-173 or MATH-182 or MATH-182A or equivalent course.) Lecture 3 (Fall, Spring).
STAT-257
Statistical Inference�
Learn how data furthers understanding of science and engineering. This course covers basic statistical concepts, sampling theory, hypothesis testing, confidence intervals, point estimation, and simple linear regression. A statistical software package such as MINITAB will be used for data analysis and statistical applications. (Prerequisites: MATH-251. NOTE: Students cannot receive credit for both MATH-252 and STAT-257 nor for both STAT-205 and STAT-257.) Lecture 3 (Fall, Spring).
STAT-305
Regression Analysis
This course covers regression techniques with applications to the type of problems encountered in real-world situations. It includes use of the statistical software SAS. Topics include a review of simple linear regression, residual analysis, multiple regression, matrix approach to regression, model selection procedures, and various other models as time permits. (Prerequisites: MATH-241 and (MATH-252 or STAT-257) or equivalent courses.) Lecture 3 (Spring).
STAT-325
Design of Experiments
This course is a study of the design and analysis of experiments. It includes extensive use of statistical software. Topics include single-factor analysis of variance, multiple comparisons and model validation, multifactor factorial designs, fixed, random and mixed models, expected mean square calculations, confounding, randomized block designs, and other designs and topics as time permits. (Prerequisites: STAT-205 or MATH-252 or STAT-257 or equivalent course.) Lecture 3 (Fall).
STAT-335
Introduction to Time Series
This course is a study of the modeling and forecasting of time series. Topics include ARMA and ARIMA models, autocorrelation function, partial autocorrelation function, detrending, residual analysis, graphical methods, and diagnostics. A statistical software package is used for data analysis. (Prerequisites: STAT-205 or MATH-252 or STAT-257 or equivalent course.) Lecture 3 (Spring).
STAT-345
Nonparametric Statistics
This course is an in-depth study of inferential procedures that are valid under a wide range of shapes for the population distribution. Topics include tests based on the binomial distribution, contingency tables, statistical inferences based on ranks, runs tests and randomization methods. A statistical software package is used for data analysis. (Prerequisites: STAT-205 or MATH-252 or STAT-257 or equivalent course.) Lecture 3 (Fall).
STAT-405
Mathematical Statistics I
This course provides a brief review of basic probability concepts and distribution theory. It covers mathematical properties of distributions needed for statistical inference. (Prerequisites: STAT-205 or MATH-252 or STAT-257 or equivalent course.) Lecture 3 (Fall).
STAT-406
Mathematical Statistics II
This course is a continuation of STAT-405 covering classical and Bayesian methods in estimation theory, chi-square test, Neyman-Pearson lemma, mathematical justification of standard test procedures, sufficient statistics, and further topics in statistical inference. (Prerequisites: STAT-405 or equivalent course.) Lecture 3 (Spring).
STAT-521
Statistical Quality Control
This course presents the probability models associated with control charts, control charts for continuous and discrete data, interpretation of control charts, and some standard sampling plans as applied to quality control. A statistical software package will be used for data analysis. (Prerequisites: MATH-252 or STAT-257 or equivalent course.) Lecture 3 (Fall, Spring).

* At least one course must be taken at the 300-level or above.

† Students may not take both STAT-257/MATH-252 and STAT-205 and receive credit.