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STA_Notes_8.29.07 - must sum to 1 3 If P(A = 1 this means A...

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STA Class 8/29/2008 Ch 3 Probability Probability permits us to make the inferential jump from sample to population and then give a measure of reliability for the inferred In this chapter we make the assumption that the population is known. 3.1 events, sample spaces, and probability Ex. Toss a fair die once and observe the up face An experiment is the process of making an observation that cannot be predicted with certainty (the toss of the die) A sample point is the most basic outcome of an experiment. The Sample space is the collection of all its sample points (observe a 1, … 2, … 3, … 4, … 5, … 6) Often we use Venn Diagrams to represent a sample space(Fig 3.1-1) Properties of probabilities (P) Given that P (A) is the probability that event A has occurred, 1. 0≤ P (A) ≤ 1 2. The probabilities of all the sample points within a sample space
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Unformatted text preview: must sum to 1 3. If P (A) = 1, this means A always happens 4. If P(A) = 0, this mean A never happens • EX. Die Toss ○ Sample Space: {1,2,3,4,5,6} what is the probability of: 1. Rolling a 5? 2. Rolling an even number? 3. Rolling a number less than 1? Note: when assigning probabilities, we use the law of large numbers— page 123 ○ Answers (fig 3.1-2) ○ Venn Diagram for Part 2 Let A = rolling an even number (fig 3.1-3) • Steps for calculating event probabilities ○ 1. Define the experiment Tossing a die ○ 2. List sample points 1,2,3,4,5,6 ○ 3. Assign probabilities 1/6 each ○ 4. What is in the event? Getting a 5 ○ 5. Sum the sample point probabilities to get the event probability STA Class 8/29/2008 1/6...
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