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14 Lecture 4 - Probability Distributions

# 14 Lecture 4 - Probability Distributions - Lecture4...

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Lecture 4: Probability Distributions &  The Sampling Distribution Introduction to Probability Distributions The Binomial Distribution The Normal Distribution The Sampling Distribution

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2 Business Statistics Agenda 1. Quiz 2! 2. Take up problems from last class 3. Special cases of the AND and OR rules 4. More on Bayes’ Theorem 5. Probability distributions 6. The Binomial distribution 7. The Normal distribution 8. Introducing the sampling distribution
Quiz 2! Duration: 25 minutes

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Let’s take 10 to relax…
5 Business Statistics Homework Finish Bayes’ problem from last class From chapter 4:  4.4 4.12 4.18 4.26 4.28 4.30

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6 Business Statistics Spotlight on Midterm ‘04 An advertising executive is studying television- viewing habits of married couples during prime- time hours. Based on past viewing records he  has determined that during prime time  husbands are watching television 60% of the  time. It has also been determined that when the  husband is watching television, 40% of the time  the wife is also watching. When the husband is  not watching television, 30% of the time the wife  is watching television.
7 Business Statistics Find the probability that: a) If the wife is watching television, the  husband is also watching television. (2  marks out of 100) b) The wife is watching television during  prime time.  (2 marks out of 100)

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8 Business Statistics Spotlight on Midterm ‘04 If  P ( A ) = 0.20,  P ( B ) = 0.30 and  P ( and  B ) = 0.06, then   A  and  B  are: a) dependent events b) independent events c) mutually exclusive events d) complementary events
Introduction to Probability  Distributions

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10 Business Statistics Some definitions What is a variable? What is a  random  variable? What is a probability distribution?
11 Business Statistics Variable Anything that can take on different values Distinguish between a  variable  and its  values A quantity:  your age the number of daily accidents on the 401  A quality:  your favourite dishwashing detergent the average grade in OMIS 1000

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12 Business Statistics Random  variable We’re now specific about the type of  values that the variable takes The values are the numerical outcomes  of a random experiment We disregard experiments with  qualitative outcomes Focus on quantitative outcomes only
13 Business Statistics Random  variable: examples The number of enrolled students who  showed up to class today:  x = {0, 1, 2, … 57} The amount of time it takes you to run a  mile: x = {x is a real number: 0 < x < infinity}

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14 Business Statistics Discrete vs. Continuous A random variable is  discrete  if it can
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