MIS 446 Lecture Notes - Lecture 7: Binomial Distribution, Continuous Or Discrete Variable, Fair Coin

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MIS 446 Advanced Business Analytics: Probability and Sampling Distributions
Agenda
oProbability and Probability Distributions
oSampling Distributions
oConfidence Interval Estimation
oSample Size Determination
Basic Probability Concepts
oProbability – the chance that an uncertain event will occur (always between 0 and 1)
oImpossible Event – an event that has no chance of occurring (probability = 0)
oCertain Event – an event that is sure to occur (probability = 1)
Events
oEach possible outcome of a variable is an event.
Simple event
An event described by a single characteristic
e.g., A day in January from all days in 2013
Joint event
An event described by two or more characteristics
e.g. A day in January that is also a Wednesday from all days in 2013
Complement of an event A (denoted A’)
All events that are not part of event A
e.g., All days from 2013 that are not in January
Probability Examples
oSuppose we roll 2 dice
Probability die rolls sum to three = 2/36
oSuppose two consumers try a new product.
Assume equally likely possible outcomes:
1. like, like
2. like, dislike
3. dislike, like
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4. dislike, dislike
oProbability at least one dislikes product = 3/4
Probability Summary
oProbability is the numerical measure of the likelihood that an event will occur
oThe probability of any event must be between 0 and 1, inclusively
oThe sum of the probabilities of all mutually exclusive and collectively exhaustive events
is 1
General Addition Rule
o
oIf A and B are mutually exclusive, then P(A and B) = 0, so the rule can be simplified:
o
o
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Review: Discrete vs Continuous Variables
oDiscrete variables produce outcomes that come from a counting process (e.g. number of
classes you are taking).
oContinuous variables produce outcomes that come from a measurement (e.g. your
annual salary, or your weight).
Discrete Random Variables
oCan only assume a countable number of values
oExamples:
Roll a die twice
Let x be the number of times 4 occurs (then x could be 0, 1, or 2 times)
Toss a coin 5 times
Let X be the number of heads (then X = 0, 1, 2, 3, 4, or 5)
oAn example of Discrete random variable probability distribution
oDiscrete Variables Expected Value
Expected Value (or mean) of a discrete variable (Weighted Average)
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