4-2_ranvar

4-2_ranvar - Lecture Unit 4 Section 4.2 Random Variables...

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Lecture Unit 4 Section 4.2 Random Variables and Probability Models: Binomial, Geometric and Poisson Distributions
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Streamline Treatment of Probability Sample spaces and events are good  starting  points for probability Sample spaces and events become quite  cumbersome when applied to real-life  business-related processes Random variables  allow us to apply  probability, risk and uncertainty to  meaningful business-related situations
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Bring Together Lecture Unit 2, and Section 4.1 In Lecture Unit 2 we saw that data could  be graphically and numerically  summarized in terms of midpoints,  spreads, outliers, etc. In Section 4.1 we saw how probabilities  could be assigned to outcomes of an  experiment. Now we bring them together
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First: Two Quick Examples 1. Hardee’s vs. The Colonel
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Hardee’s vs The Colonel Out of 100 taste-testers, 63 preferred  Hardee’s fried chicken, 37 preferred KFC Evidence that Hardee’s is better? A  landslide ? What if there is no difference in the  chicken? (p=1/2, flip a fair coin) Is 63 heads out of 100 tosses that  unusual?
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Example 2. Mothers Identify Newborns
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Mothers Identify Newborns After spending 1 hour with their newborns,  blindfolded and nose-covered mothers were  asked to choose their child from 3 sleeping  babies by feeling the backs of the babies’ hands 22 of 32 women (69%) selected their own  newborn “far better than 33% one would expect …” Is it possible the mothers are guessing? Can we quantify “far better”?
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Graphically and Numerically Summarize a Random Experiment Principal vehicle by which we do this: random variables A random variable assigns a number  to  each outcome of an experiment
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Random Variables Definition: A random variable is a numerical-valued  function defined on the outcomes of an  experiment S Number line Random variable
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Examples S = {HH, TH, HT, TT} the random variable:  x = # of heads in 2 tosses of a coin Possible values of x = 0, 1, 2
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Two Types of Random Variables Discrete: random variables that have a  finite or countably infinite number of  possible values Test: for any given value of the random  variable, you can designate the next  largest or  next smallest value of the  random variable
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Examples: Discrete rv’s Number of girls in a 5 child family Number of customers that use an ATM in  a 1-hour period.
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4-2_ranvar - Lecture Unit 4 Section 4.2 Random Variables...

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