STAT 511 (Spring 2025, Section 6)
Statistical Methods
Lecture Notes
Chapter 1: overview.
Sections 2.1 and 2.2: definition of probability.
Section 2.3: counting techniques.
Section 2.4: conditional probability.
Section 2.5: independence.
Section 3.1: Random variable.
Section 3.2: Probability Distributions for Discrete Random Variables.
Section 3.3: Expected value of Discrete Random Variables.
Section 3.4: The Binomial Probability Distribution.
Section 4.3: The Normal Distribution.
Section 5.1: Joint Distribution of Random Variables.
Section 5.2: Expected Values, Covariance, and Correlation.
Section 5.4: The Distribution of the Sample Mean.
Section 5.5: The Distribution of a Linear Combination.
Section 7.1: Basic Properties of Confidence Interval.
Section 7.2: Large-Sample Confidence Intervals for a Population Mean and Proportion.
Section 7.3: Interval based on a normal population distribution.
Section 7.4: Confidence Interval for Variance and Standard Deviation of a Normal Population.
Section 8.1: Hypotheses and Testing Procedure.
Section 8.2: z-Test about a Population Mean.
Section 8.3: The One-Sample t Test.
Section 8.4: Testing Concerning a Population Proportion.
Section 9.1: z-test and Confidence Interval for a Difference Between Two Population Means.
Section 9.2: The Two-sample t Test and Confidence Interval.
Section 9.3: Analysis of Paired Data.
Section 9.4: Inference Concerning a Difference Between Population Proportions.
Section 9.5: Inferences Concerning Two Population Variances.
Chapter 12: Simple Linear Regression and Correlation and R code.