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Random Phenomena Outcome is unknown before the event Flipping a coin Rolling a die Taking a sample from a population Long term behavior is predictable 50% heads 16.67% for 1, 2, 3, 4, 5, or 6 Sampling Distribution (Chapter 18) 1 Probability Subjective (Personal) Based on feeling or opinion. Empirical Based on experience. Theoretical (Formal) Based on assumptions. 2 Chips Example Bag o‟ chips (poker chips). Some are red. Some are white. Some are blue. Draw a chip from the bag. We don‟t know how many of each of the three colors are in the bag. Assumption: Each chip has equal probability of being chosen (Same size, same weight, same texture, etc.) 3 The Deal Possible out comes of the draw Draw a blue chip win 3 bonus points. Draw a red chip win 2 bonus points. Draw a white chip lose 3 bonus points. 4 Is this a good deal? Subjective (personal) probability Based on your beliefs and opinion. Empirical probability Based on experience. Conduct a series of trials. Each trial has an outcome (R, W, B). 5 Empirical Probability Look at the long run relative frequency of each of the outcomes after choosing n=50 with replacement. Blue Red White 6 Theoretical Probability Look in the bag and see how many Blue chips – Red chips – White chips – Assumption Each chip has the same probability of being chosen. Equally likely. 7 Law of Large Numbers For repeated independent trials, the long run relative frequency of an outcome gets closer and closer to the true probability of the outcome. How does this compare with the “Law of Averages”? 8 Law of Large Numbers Probability is a long term number Ex. Flip a coin 5 times and get 5 heads in a row, is a tail due on next flip? Random events do not compensate for short term behavior Over a long sequence of flips, even after a sequence of many heads in a row, P(tails after sequence) = 0.5 9 Law of Large Numbers Over the long term, P(heads) = 0.5 Long term - Infinite 10 Probability Rules A probability is a number between 0 and 1. Something has to happen rule. The probability of the set of all possible outcomes of a trial must be 1. 11 Probability Rules Event – a collection of outcomes. Win bonus points (Blue or Red chip) Complement rule The probability an event occurs is 1 minus the probability that it doesn‟t occur. P(A) = 1 – P(AC) 12 Probability Rules Disjoint events – no outcomes in common. Addition Rule for disjoint events. P(A or B) = P(A) + P(B) P(Blue or Red) = P(Blue) + P(Red) 13 Probability Rules Independent outcomes - The outcome of one trial does not influence the outcome of the other. 1) Coin flips as „Head‟ and 2) Coin flips as „Head‟. INDEPENDENT: The outcome of flipping a coin does not depend on the previous coin flip outcome. 1) It snows or not and 2) Class is cancelled or not NOT INDEPENDENT: The outcome of 2) depends on the outcome of 1). 14 Probability Rules Independent trials Multiplication rule for independent trials. P(1st outcome and 2nd outcome) = P(1stoutcome)*P(2nd outcome) 15 Example What is the chance that two people in a row win bonus points? P(win 1st and win 2nd)=P(win 1st)*P(win 2nd) P(win 1st) = P(Blue or Red) = P(Blue)+P(Red) P(win 2st) = P(Blue or Red) = P(Blue)+P(Red) 16 Three Terms to Look For. Not This means the compliment that is subtract form 1. Or This means to add the probabilities. And This means to multiply the probabilities. 17

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probability theory, possible outcomes, sample space, the experiment, Conditional Probability, probability distributions, Empirical Probability, Introduction to Probability, probability and statistics, multiplication rule

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posted: | 2/5/2010 |

language: | English |

pages: | 17 |

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