4-2_ranvar

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

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Unformatted text preview: Lecture Unit 4 Section 4.2 Random Variables and Probability Models: Binomial, Geometric and Poisson Distributions 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 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 First: Two Quick Examples 1. Hardees vs. The Colonel Hardees vs The Colonel Out of 100 taste-testers, 63 preferred Hardees fried chicken, 37 preferred KFC Evidence that Hardees 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? Example 2. Mothers Identify Newborns 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? 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 Random Variables Definition: A random variable is a numerical-valued function defined on the outcomes of an experiment S Number line Random variable 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 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 Examples: Discrete rvs Number of girls in a 5 child family Number of customers that use an ATM in a 1-hour period. Number of tosses of a fair coin that is required until you get 3 heads in a row (note that this discrete random variable has a countably infinite number of possible values: x=3, 4, 5, 6, 7, . . . ) Two types (cont.) Continuous: a random variable that can...
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4-2_ranvar - Lecture Unit 4 Section 4.2 Random Variables...

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