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

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Presentation transcript:

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

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.

The probability distribution shows k possible values of the random variable X along with the corresponding probabilities. The mean of the random variable X, denoted by ____, is found using the formula: In words, Value of x….. Probability….. multiply each value of X times its probability and add all these products together.

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.

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.

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.

TI83/84: Put x’s in L1 and P(x)s in L2 STAT / CALC 1:1-Var Stats ENTER 1-Var Stats L1, L2