# Math 218, Mathematical Statistics

## Syllabus

### Spring 2016 Professor D Joyce BP 322 Department of Mathematics and Computer ScienceClark University

• Chapter 1: Introduction (1 meeting)
The basic goal of statistics: draw conclusions based on data. There are various aspects of statistics ranging from formulating the question, designing experiments to address the question, collecting the data, and analyzing the data, but we'll be stressing the role of probability and probability distributions in this process. We'll often begin with a random sample drawn from a parameterized family of distributions, and our job is to make conclusions about the parameter.

• Chapter 2: Review of Probability (1 meeting)
We'll quickly review the theory of probability. Sample spaces and events, Kolmogorov's axioms, principles of combinatorics including permutations and combinations, conditional probability and independence, Bayes' theorem, random variables, probability mass functions for discrete random variables, probability density functions for continuous random variables, cumulative distribution functions, expected value, mean and variance of a distribution, selected discrete and continuous distributions.

• Chapter 3: Collecting Data (2 meetings)
Types of statistical studies, observational studies, basic sampling designs

• Chapter 4: Summarizing and Exploring Data (2 meeting)

• Chapter 5: Sampling Distributions of Statistics (6 meetings)
• 5.1. Sampling Distribution of the Sample Mean
• 5.2. Sampling Distribution of the Sample Variance
• 5.3. Student's t-distribution
• 5.4. Snedecor-Fisher's F-distribution

• Chapters 6 and 15: Basic Concepts of Inference (7 meetings)
• 6.1. Point Estimation
• 15.1. Maximum Likelihood Estimation
• 6.2. Confidence Interval Estimation
• 6.3. Hypothesis Testing
• 15.2. Likelihood Ratio Tests

• Chapter 7: Inferences for Single Samples (4 meetings)
• 7.1. Inferences on Mean (Large Samples)
• 7.2. Inferences on Mean (Small Samples)
• 7.3. Inferences on Variance (if time permits)

• Chapter 8: Inferences for Two Samples (4 meetings)
• 8.1. Independent Samples and Matched Pairs Designs
• 8.2. Graphical methods for comparing two samples
• 8.3. Comparing Means of Two Populations, independent samples and matched pairs

• Chapter 9: Inferences for Proportions and Count Data (3 meetings)
• 9.1. Inferences on Proportion
• 9.2. Inferences on Comparing Two Proportions

• Chapter 10: Simple linear regression and correlation (4 meetings)
• The least squares method
• 10.1. The model for simple linear regression
• 10.2. Fitting a line, goodness of fit
• 10.3. Statistical inference with the simple linear regression model, prediction and confidence intervals
• 10.4. Regression diagnostics

• Chapter 11: Multiple linear regression and (3 meetings)
• 11.1. The model for multiple linear regression
• 11.2. Goodness of fit, multiple correlation coefficient
• 11.3. Arrays, matrices, and linear algebra for multiple linear regression
• 11.4. Statistical inference for multiple regression, ANOVA tables

• An Introduction to Bayesian Inference (4 meetings)
• 15.3. Principles of Bayesian statistics. The Bernoulli process.
• The Poisson process. The normal process.