Section 5.1-5.2 - Chapter 5:Probability & Sampling...

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Chapter 5:Probability Chapter 5 onwards, we make the transition from Descriptive Statistics to Inferential Statistics . Statistic : Any calculated measure from a random sample (sample mean, sample SD, sample proportion, correlation coefficient, etc.) is called a statistic. Inferential statistics is a branch of statistics that deals with methods to make inferences about the population parameters, from sample statistics. 5.1 Chance Experiment We discuss in this section (i) Random Experiments (ii) Events: Simple Events and Events (iii)Sample Space (iv)Tree Diagram (v)Venn Diagram 1
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With random samples , our conclusions can be extended to the population; otherwise, they are only summaries for that particular data set only. Probability methods help us to to evaluate the reliability and confidence of the sample statistics. Random (Chance) Experiment : An experiment (process, situation) whose outcomes are known but can not be predicted in advance. Chance experiments arise of natural phenomena or we introduce for Inference purpose. Probability is a way modeling of outcomes of a random experiment. First we define the concepts: (i) Sample Space; (ii) Event ; (iii) Probability Sample space (S): the set of all possible outcomes (simple events) of a random experiment. A simple event (e) : An individual outcomes of an experiment Events (A, B, C, …): It is a simple event or a set of simple events. 2
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Example 1. Experiment: A single die rolled Sample space: S = { 1, 2, 3, 4, 5, 6} Simple events: {1}, {2}, … , {6}. An event: A= {2, 4, 6}= An event of getting an even integer. Note A is a set of simple events or a subset of S. Example 2 . Two dice are rolled. Sample space: S = { (1,1), (1,2), …, (6,6)}. Simple events (examples): (3,4) or (5,6) or (6, 6). An event:
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This note was uploaded on 07/25/2008 for the course STT 351 taught by Professor Palaniappan during the Summer '08 term at Michigan State University.

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Section 5.1-5.2 - Chapter 5:Probability & Sampling...

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