38 - Chapter 5 Probability in our Daily Lives Section 5.1...

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Unformatted text preview: Chapter 5 Probability in our Daily Lives Section 5.1: How can Probability Quantify Randomness? Learning Objectives 1. Random Phenomena 2. Law of Large Numbers 3. Probability 4. Independent Trials 5. Finding probabilities 6. Types of Probabilities: Relative Frequency and Subjective Learning Objective 1: Random Phenomena For random phenomena, the outcome is uncertain In the short-run, the proportion of times that something happens is highly random In the long-run, the proportion of times that something happens becomes very predictable Probability quantifies long-run randomness Learning Objective 2 : Law of Large Numbers As the number of trials increase, the proportion of occurrences of any given outcome approaches a particular number “in the long run” For example, as one tosses a die, in the long run 1/6 of the observations will be a 6. Learning Objective 3: Probability With random phenomena, the probability of a particular outcome is the proportion of times that the outcome would occur in a long run of observations Example: When rolling a die, the outcome of “6” has probability = 1/6. In other words, the proportion of times that a 6 would occur in a long run of observations is 1/6. Learning Objective 4 : Independent Trials Different trials of a random phenomenon are independent if the outcome of any one trial is not affected by the outcome of any other trial. Example: If you have 20 flips of a coin in a row that are “heads”, you are not “due” a “tail” - the probability of a tail on your next flip is still 1/2. The trial of flipping a coin is independent of previous flips. Learning Objective 5: How can we find Probabilities? Calculate theoretical probabilities based on assumptions about the random phenomena. For example, it is often reasonable to assume that outcomes are equally likely such as when flipping a coin, or a rolling a die. Observe many trials of the random phenomenon and use the sample proportion of the number of times the outcome occurs as its probability. This is merely an estimate of the actual probability. Learning Objective 6 : Types of Probability: Relative Frequency vs. Subjective The relative frequency definition of probability is the long run proportion of times that the outcome occurs in a very large number of trials - not always helpful/possible. When a long run of trials is not feasible, you must rely on subjective information. In this case, the subjective definition of the probability of an outcome is your degree of belief that the outcome will occur based on the information available. Bayesian statistics is a branch of statistics that uses subjective probability as its foundation Chapter 5: Probability in Our Daily Lives Section 5.2: How Can We Find Probabilities? Learning Objectives 1. Sample Space 2. Event 3. Probabilities for a sample space 4. Probability of an event 5. Basic rules for finding probabilities about a pair of events Learning Objectives 1. Probability of the union of two events 2. Probability of the intersection of two events Learning Objective 1 : Sample Space For a random phenomenon, the sample space is the set of all possible outcomes. Learning Objective 2...
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38 - Chapter 5 Probability in our Daily Lives Section 5.1...

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