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day8 - The goal of statistics In order to use the sample to...

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The goal of statistics: In order to use the sample to draw inferences or make conclusions about the population we need to understand probability . Probability Probability is a numerical measure of the likelihood that an event will occur. Examples : Experiment : a process that generates well deﬁned outcomes. Only one of the possible outcomes occurs on a single repetition of the ex- periment. Examples : 1

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Sample Space : the set of all outcomes Examples : Often in order to discuss probabilities of outcomes we need to know how many possible outcomes there are. Counting rules for Outcomes 1. Multi-step Experiments Ex : Tossing two coins 2. Suppose an experiment can be described as a sequence of k steps. Let n 1 be the number of possible outcomes for step 1, n 2 be the number of possible outcomes for step 2, etc. Then Total number of outcomes = n 1 n 2 ··· n k . Ex : In the city of Milford, applications for zoning changes go through a two-step process: a review by the planning commission and a ﬁnal deci- sion by the city council. At step 1 the planning commission reviews the zoning change request and makes a positive, neutral, or negative recom- mendation. At step 2 the city council reviews the planning commission’s
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day8 - The goal of statistics In order to use the sample to...

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