# 2.1-2.2 - Chapter 2:Probability Chapter 2 onwards we make...

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Chapter 2:Probability Chapter 2 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. 2.1 Sample space and events 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 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 of modeling 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 outcome of an experiment Events (A, B, C, …): It is a simple event or a set of simple events. 2
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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2.1-2.2 - Chapter 2:Probability Chapter 2 onwards we make...

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