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Alex Lun (4)
Lecture 3

Week 3 EC255.docx

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Alex Lun

EC255 Week 3 4.8 REVISION OF PROBABILITIES: BAYES’ RULE -a formula that extends the use of the law of conditional probabilities to allow revision of original probabilities with new information -The denominator of Bayes’ rule includes a product expression for every partition in the sample space Y, including the event X itself -The denominator is a collectively exhaustive listing of mutually exclusive outcomes of Y -Staticians use Bayes’ rule to “revise” probabilities in light of new information -Bayes’ rule provides a way of incorporating prior knowledge into our calculations. Or this reason, it can be a valuable tool in decision making 5.1 DISCRETE VERSUS CONTINUOUS DISTRIBUTIONS -A random variable is a variable that contains the outcomes of a chance experiment. Ex. 1 car, 2 cars, n cars… -The two categories of random variables are discrete and continuous -A discrete random variable is if the set of all possible values is at most a finite or a count ably infinite number of possible values. In most situations, discrete random variables product values that are nonnegative whole numbers. Ex. If 6 people are randomly selected to be determined if they are left- handed, it is discrete because the only possibilities are in the sample of 6: 0,1,2,3,4,5,6 – there cannot be 2.75 left-handed people -Continuous random variables take on values at every point over a given interval. Ex. 8.67 seconds. Ex. Measuring the supply of volume of liquid nitrogen in a storage tank. -Ex. Discrete distrib
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