AEM 201 1st Edition Lecture 10PREVIOUS LECTUREI. Introduction To ProbabilityII. Counting RulesIII. Methods Of Assigning Probability To Experimental OutcomesIV. Relationship Of ProbabilityCURRENT LECTUREI. Relationship of ProbabilityII. Discrete Probability of DistributionRELATIONSHIP OF PROBABILITY- Addition Law: for 2 events A and B:o We must subtract the intersection (joint probability)o Subtracting the items that were counted twice-if you don’t subtract them out then you are double counting- Addition Law of Mutually Exclusive Events: for two mutually exclusive event A and B:- We don’t have to subtract because there is no intersection- The addition law ALWAYS works, the addition law of mutually exclusive events is just a short cut when you KNOW there is no intersection- Conditional Probability: the probability that one event A will occur given some event B has occurred or will occur- We can use the concept of P(B) conditional probability to define independent events- Independent Events: two events A and B such that the probability that one event say A will occur does not change whether or not the other event B occurso The probability of A does not change by knowing Bo The probability of A give B still equals the probability of AGradeBuddy- If the probability of A does not equal the probability of A given B then the twoevents are not independent- Note we have estimated the probability through an experiment and must be concerned with whether the difference between the probability of A and Probability of A given B is sufficient for us to conclude with confidence the events are not independent- Multiplication Law: For two events A and B:- Multiplication Law for Independent Events: for two events A and B- The multiplication law will ALWAYS work. If you know events are independent then you can use a short cut- These are for intersections- Simpson’s Paradox: the reversal of the direction of a comparison or an association when data from several groups are combined to form a single groupDISCRETE PROBABILITY DISTRIBUTION- Random Variable: a numerical description of the outcome of an experiment- Discrete Random Variable: a numerical description of the outcome of an experiment that can yield only a finite number of values or an infinite sequence- Continuous Random Variable: a numerical description of the outcome of an experiment whose outcome can assume any numerical value in an interval or collection of intervals- Probability Distribution: description of how probabilities are allocated to potential values of a random
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