• 2023 Putnam Competition Result

    We very excited to report that our Putnam team ranked 8th, honorable mention, among 471 institutions in the 2023 Putnam math competition.Our team members this year were Vincent Trang, Daniel Yuan, Omar Habibullah, and Andrew Parker.Vincent Trang ranked 43rd and Daniel Yuan ranked 64th among 3,857 participants. Read More
  • Simons Fellows - Darvas, Kanigowski, Rubinstein

    Congratulations to Tamas Darvas, Adam Kanigowski, and Yanir Rubinstein for being named Simons Fellows. Read More
  • Doron Levy is elected 2024 Class of Fellows of the AMS

    Congratulations to Dr. Doron Levy, as Fellow of the American Mathematical Society, Class of 2024 (https://www.ams.org/cgi-bin/fellows/fellows_by_year.cgi)!  Dr. Levy was elected  ``For his contributions to Mathematical Oncology and Mathematical Biology".  Read More
  • Scott Wolpert to lead NSF-funded project on DEI in mathematics and statistics

    Congratulations to Scott Wolpert, professor emeritus of mathematics, who was named principal investigator of a new project to improve diversity, equity and inclusion in mathematics departments. The project is funded by a $600,000 grant from the NSF, and it will provide DEI training to six representatives of math and statistics departments Read More
  • Abba Gumel Featured in Scientific American Article

    Congratulations to Abba Gumel being featured in a new Scientific American Article. The title is “How Mathematics Can Predict and Help Prevent the Next Pandemic” (link to the article). What a great advertisement to Maryland. It is a great honor to have Abba as our colleagues.   Congratulations Abba! Read More
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Description

Stat 400 is an introductory course to probability, the mathematical theory of randomness, and to statistics, the mathematical science of data analysis and analysis in the presence of uncertainty. Applications of statistics and probability to real world problems are also presented.

SUPPLEMENTAL MATERIALS:

Transformation of random variables (Slud)

Computer simulation of random variables (Slud)

The Law of Large Numbers (Boyle)

The Central Limit Theorem (Boyle)

Prerequisites

1 course with a minimum grade of C- from (MATH131, MATH141)


Level of Rigor

Standard


Sample Textbooks

Probability and Statistics for Engineering and the Sciences, by J. Devore. 

STAT 400 + ENHANCED WEBASSIGN(IP), by J. Devore


Applications

Engineering, computer science, philosophy, chemistry, economics, business


If you like this course, you might also consider the following courses



Additional Notes

Duplicate credit with BMGT231 and ENEE324

Topics

Data summary and visualization

Sample mean, median, standard deviation

*Sample quantiles, *box-plots

(Scaled) relative-frequency histograms

Probability

Sample space, events, probability axioms

Probabilities as limiting relative frequencies

Counting techniques, equally likely outcomes

Conditional probability, Bayes' Theorem

Independent events

*Probabilities as betting odds

Discrete Random Variables

Distributions of discrete random variables

Probability mass function, distribution function

Expected values, moments

Binomial, hypergeometric, geometric, Poisson distributions

Binomial as limit of hypergeometric distribution

Poisson as limit of binomial distribution

*Poisson process

Continuous Random Variables

Densities: probability as an integral

Cumulative distribution, expectation, moments

Quantiles for continuous rv's

Uniform, exponential, normal distributions

*Gamma function and gamma distribution

*Other continuous distributions

*Transformation of rv's (by smoothly invertible functions): distribution function and density

*Simulation of pseudo-random variables of specified distribution (by applying inverse dist. func. to a uniform pseudo-random variable)

Joint distributions, random sampling

Bivariate rv's, joint (discrete) probability mass functions

*Expectation of function of jointly distributed rv's

*Joint and marginal densities

*Correlation, *covariance

Mutually independent rv's. Mean and variance of sums of independent rv's

*Sums of rv's, laws of expectation

Law of Large Numbers, Central Limit Theorem

Connection between scaled histograms of random samples and probability density functions

Point estimation

Populations, statistics, parameters and sampling distributions

Characteristics of estimators : consistency, accuracy as measured by mean square error, *unbiasedness

Use of Central Limit Theorem to approximate sampling distributions and accuracy of estimators

Method of moments estimator

*Maximum likelihood estimator

*Estimators as population characteristics of the empirical distribution

Confidence intervals

Large sample confidence intervals for means and proportions using Central Limit Theorem

*Small sample confidence intervals for normal populations using Student's t distribution

Confidence interval as decision procedure/hypothesis test

Hypothesis Tests

*Hypothesis testing definitions (Null and alternate hypotheses, Type I and II errors, significance level and power, p-values)

*Tests for means and proportions in large samples, based on the Central Limit Theorem

*Small sample tests for means of normal populations using Student's t distribution

*Exact tests for proportions based on binomial distribution


* = optional


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