Chapter3 Examples and Notes(2)

Chapter3 Examples and Notes(2) - Chapter 3 Examples and...

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Chapter 3 Examples and Notes (will be updated regularly) Section 3.1 Experiment: It is an action or a process which generates outcomes (data), however they cannot be predicted for certain. Note: The uncertainty of an experiment may be measured using the probability concept. In general it is the chance or likelihood that an outcome or an event occurs. Definitions: Sample Space (S): It is the complete list of all outcomes of an experiment Event : It is a subset of a sample space. Events are denoted by capital letters. Sample Point / Simple Event : It is a single outcome of an experiment Note: Helps to know the counting principles: Permutations, Combinations , and fundamental principle of counting. Probability of an event can be assigned by 3 different methods: Theoretical Probabilities; Objective probabilities; Subjective probabilities Note: It is general practice that probability is denoted by P and probability of an event A is denoted by P(A). To calculate the probabilities of outcomes or events, follow the steps 1. Understand the experiment 2. Write the S 3. Write the event of interest 4. Assign the probabilities to each sample point (each outcome) 5. If an event is made of multiple sample points, then the probability of the event is sum of the probabilities of sample points in the event. Note: Step 4 is not always obvious. Requires the knowledge about the experiment and outcomes. However, in the case of equally likely outcomes , the probabilities of simple events can be easily assigned. Equally Likely Outcomes : All outcomes of an experiment are equally likely to occur. Equally Likely Events: All events of an experiment are equally likely to happen Suppose { } k o o o S , , , 2 1 = and all outcomes are equally likely, then the probability of any simple event in this S is 1/k, where k is the number of outcomes. If all outcomes of in a S are equally likely then Probability of an Event A,
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P(A) = S in outcomes of count A in outcomes of count Theoretical Probabilities (Probability Rules) Suppose { } k o o o S , , , 2 1 = then probabilities can be assigned using the following rules: 1. 1 ) ( 0 j o P 2. 1 ) ( ) ( ) ( ) ( ) ( 2 1 1 = + + + = = = k n i i o P o P o P o P S P The following concepts help through out the chapter. 1. A sample (subject) from a population is selected RANDOM implies chance of selecting this subject is same as chance of selecting any other subject in the population. Note: A Population is a collection of all subjects of interest. Subjects could be people or things. With replacement : If each member of a population is replaced after it is picked, then that member has the possibility of being chosen more than once. When sampling is done with replacement, then events are considered to be independent, meaning the result of the first pick will not change the probabilities for the second pick. Without replacement:
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Chapter3 Examples and Notes(2) - Chapter 3 Examples and...

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