EC255 Lecture Notes - Lecture 3: Geometric Distribution, Standard Deviation, Binomial Distribution

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Published on 12 Oct 2012
School
WLU
Department
Economics
Course
EC255
Professor
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 distributions binomial distribution, poisson distribution, hyper geometric distribution
-Ex. Continuous distributions: uniform, normal, exponential, t, chisquare, F
5.2 DESCRIBING A DISCRETE DISTRIBUTION
-The histogram is probably the most common graphical way to depict a discrete distribution
Mean, Variance, and Standard Deviation of Discrete Distributions
-The measures of central tendency can be applied to discrete distributions to compute a mean, a
variance, and a standard deviation
5.2 BINOMIAL DISTRIBUTION
Assumptions of the binomial distribution:
-The experiment involves n identical trials
-Each trial has only two possible outcomes denoted as success or as failure
-Each trial is independent of the previous trials
-The terms p and q remain constant throughout the experiment, where the term p is the probability of
getting success on any one trial and the term q= l-p is the probability of getting a failure on any one trial
-Any single trial of a binomial experiment contains only two possible outcomes these are labelled
success and failure
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Document Summary

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. A random variable is a variable that contains the outcomes of a chance experiment. 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.

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