Rose-Hulman - Department of Mathematics - Course Syllabus
MA381 - Introduction to Probability with Applications to Statistics -
Parts of the web page to be completed or determined by the instructor are in green.
Catalogue Description and Prerequisites
MA 381 Introduction to Probability with Applications to Statistics 4R-0L-4C F,W,S
Pre: MA 113
Introduction to probability theory; axioms of probability, sample spaces, and
probability laws (including conditional probabilities). Univariate random variables
(discrete and continuous) and their expectations including these distributions:
binomial, Poisson, geometric, uniform, exponential, and normal. Introduction
to moment generating functions. Introduction to jointly distributed random variables.
Univariate and joint transformations of random variables. The distribution of
linear combinations of random variables and an introduction to the Central Limit
Theorem. Applications of probability to statistics.
Prerequisite: Calculus III - MA113
An understanding of the ideas of probability and probability modeling,
including sample spaces, axioms, discrete and continuous random variables,
univariate and joint distributions, moment generating functions, the central
limit theorem, and basic statistical inference
- An understanding
of the special language, notation, and point of view of probability
understanding of the concepts of probability necessary to undertake basic
modeling and decision making in math, science, and engineering
ability to solve standard computational problems in probability, which
includes using the computer as a tool for mathematical analysis and
- An understanding of the relationship between random variables
and their distribution functions
- The ability to recognize special
models, such as Bernoulli trials or Poisson processes
understanding of how probability is applied to inferential statistics
- The ability to communicate in mathematical terms
Textbook and other required materials
Textbook: Fundamentals of Probability
with Stochastic Processes, 3rd edition, by Saeed Ghahramani
Computer Usage: Maple may be used during the course
to help with various calculations.
The course will cover the following chapters and topics from the textbook:
Sample Space, Events, Axioms of Probability
Counting Principles, combinations, permutations
Probability, laws of multiplication and total probability, Bayes' Formula,
Variables, distribution functions, discrete random variables, expectation
of discrete random variables, variances and moments of discrete random
variables, standardized random variables.
- Special Discrete Distributions: Bernoulli
and Binomial, Poisson (including Poisson Process), Geometric
- Continuous Random Variables: Probability
density functions, density function of a function of a random variable,
expectation and variances
- Special Continuous Distributions: Uniform,
Normal , Exponential
- Bivariate Distributions: Joint
distributions, independent random variables, conditional distributions
Transformations of 2 random variables
values of sums of random variables, covariance, correlation, conditioning
on random variables
generating functions, sums of independent random variables, Markov and Chebyshev
inequalities, Central Limit Theorem
- Estimators and Confidence Intervals topics selected from
- Estimators of mean μ, variance σ 2
and Bernoulli parameter p
- Unbiased Estimators
- Confidence intervals for mean µ given normal
population with known variance
- Use of confidence intervals to do hypothesis
- Sample size calculations
- Confidence interval for difference of two
means from different normal populations
Course Requirements and Policies
The following policies and requirements will apply to all sections and classes:
- Maple will be used to help with various calculations during the course.
- However, emphasis will be placed on the mathematical derivation and simplification of formulas and expressions without the use of technology.
Final Exam Policy
The final exam will cover all material from the course. The use of Maple
may be allowed, but not emphasized. For full credit to be awarded for
any given problem, all work must be shown.
Individual Instructor Policies
Your instructor will determine the following for your class:
*Note that most instructors will enforce some type of grade penalty for students with more than four unexcused absences.
- the grading scheme, based on the various course components.
- the number and format of hour exams, quizzes, homework assignments, in class assignments, and projects,
- the policies governing the work items above, e.g.,
- all policies for classroom procedure, including group work, class participation, laptop use and attendance*.