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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