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AP Statistics Section 7.2A Mean & Standard Deviation of a Probability Distribution

AP Statistics Section 7.2A Mean & Standard Deviation of a Probability Distribution.

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AP Statistics Section 7.2A Mean & Standard Deviation of a Probability Distribution

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  1. AP Statistics Section 7.2AMean & Standard Deviation of a Probability Distribution

  2. The mean, ,of a set of observations is simply their ordinary average. The mean of a random variable X is also an average of the possible values of X, BUT we must take into account that the various values of X are not all equally likely.

  3. The probability distributionshows k possible values of therandom variable Xalong with the corresponding probabilities.The mean of the random variable X, denoted by ____, is found using the formula:In words, multiply each value of X times its probability and add all these products together.

  4. The mean of a random variable X is also called the expected value, because it is the “average” we would expect to get with infinitely any trials.

  5. To find the variance of a discrete random variable ( __ ), use the formula:Recall that the standard deviation of X (__) is the square root of the variance.

  6. Example: Consider the probabilities at the right for the number of games, X, it will take to complete the World Series in any given year.Determine the mean and standard deviation of X. # of games Prob. 4 .1819 5 .2121 6 .2323 7 .3737

  7. TI83/84: Put x’s in L1 and P(x)s in L2STAT / CALC 1:1-Var Stats ENTER1-Var Stats L1, L2

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