A mouse moves along a tiled corridor with 2m tiles, where m > 1. From each tile i l' 1, 2m. it moves to either tile i - l or i + 1 with equal probability. From tile 1 or tile 2m, it moves to tile 2 or 2m - 1, respectively, with probability 1. Each time the mouse moves to a tile i $ m or i > m, an electronic device outputs a signal L or R, respectively. Can the generated sequence of signals L and R be described as a Markov chain with states L and R?
Chapter 1 Throughout the semester, we will learn methods to address questions such as these. To get started, we need to learn some basic vocabulary. -Subject: entities that we measure in a study -Variable: any characteristic that is observed for the subject in a study -Population: a set of all subjects of interest -Sample: the set of subjects for which we have data **We want to use the sample’s data to make an inference about the population.** -Statistic: a numerical summary of the sample (known information) -Parameter: a numerical summary of the population (unknown information) There are 3 major components to Statistics: 1. Design of the Study • What is the research question • What is/are the population of interest • What is the
