lecture_4_4 - Probability and inference Mean and Variance...

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    Probability and inference Mean and Variance of Random variables IPS chapter 4.4 © 2006 W.H. Freeman and Company
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Objectives Mean of a random variable Variance of a random variable Rules for means and variances of random variables
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Example: Lotteries -Tri-State Pick 3 Choose a three digit number (000-999) A randomly chosen 3 digit number wins and gets $500. Probability 1/1000 of winning $500. X is a random variable – the amount that your ticket pays. Probability distribution of X Average payoff from many tickets (long run average payoff)? Payoff X $0 $500 Probability 0.999 0.001
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Mean of a random variable The mean x bar of a set of observations is their average. The mean µ of a random variable X is a weighted average of the possible values of X , reflecting the fact that all outcomes might not be equally likely. Value of X 0 1 2 3 Probability 1/8 3/8 3/8 1/8 HMM HHM MHM HMH MMM MMH MHH HHH A basketball player shoots three free throws. The random variable X is the number of baskets successfully made (“H”). The mean of a random variable X is also called expected value of X .
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Mean of a discrete random variable For a discrete random variable X with
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