Module 4 Help Session S18.pdf

Module 4 Help Session S18.pdf - PHC 4069 Biostatistics in...

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PHC 4069 Biostatistics in Society Module 4 Help Session Probability Created by: Hanze Zhang Presented: Ying Ma
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Statistics Descriptive Collecting, organizing Summarizing, presenting Inferential Hypotheses Relationships predictions Modules 1, 2 and 3 Modules 7-10 Probability: Modules 4-6 Rough Overview of the course
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Probability: how likely or unlikely are the possible outcomes of a random phenomenom Random phenomenon: Individual outcomes are not predictable but... Probabilities associated with each possible outcome are well defined Example: roll a “fair” die 6 sides we know that in the long run each of the six sides has a probability of being face up (1/6) Random vs. Haphazard phenomena
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Probability: how likely or unlikely are the possible outcomes of a random phenomenom Haphazard phenomenon: Probabilities associated with each possible outcome are unknown Example: ask someone to pick number from 1 to 6 unpredicatable do not know the probability that he/she will pick any of the values Random vs. Haphazard phenomena
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Probability distribution of random variables Random sample- random variables random phenomena Random variables: quantitative representations of random phenomena Two components of a probability distribution: 1. Sample space : list of all possible outcomes Roll a fair die once: sample space= {1,2,3,4,5,6} 2. Probability of each outcome: (1/6) for the fair die Event= a combination of outcomes from a random phenomenon
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Basic rules of probability
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Union of events The combination of the events outcomes Disjoint events: events that do not have any outcomes in common. Example: roll a fair die Event A: getting “3” Event B: getting “6” Simple addition rule of probability P[A or B] = P[A] + P[B] = 1/6 + 1/6 =2/6 in this example
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Intersection of events Porbability that all events will occur Independent events: probability of event B occuring does not depend on the probability of event A occurring, or vice- versa. Example: flip a coin, whether or not the first toss is {heads} is not related to whether the second toss is {heads} or {tail} Simple multiplication rule of probability: P[A and B] = P[A] X P[B]
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Theoretical vs. Empirical probabilities of a random variable Theoretical probabilities: based on assumptions about 1) The nature of the random phenomenon 2) Rules of probability and 3) Logic If 1, 2 and 3 are valid then theoretical probabilities are correct.
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Theoretical vs. Empirical probabilities of a random variable Empirical probabilities: derived from observations of many outcomes of the random phenomenon Relative frequency of a specific event out of the toal number of observations=estimate of the probability of that event.
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