Section 7.2.2 Means and Variances of Random Variables AP Statistics www.toddfadoir.com/apstats.

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Presentation transcript:

Section Means and Variances of Random Variables AP Statistics

AP Statistics, Section 7.2, Part 12

3 Rules for Means Rule 1: The same scale change of elements of a probability distribution has the same effect on the means. Rule 2: The mean of sum of the two distributions is equal to the sum of the means.

AP Statistics, Section 7.2, Part 14 Rule 1 Example A company believes that the sales of product X is as follows. X ,000 P(X)

AP Statistics, Section 7.2, Part 15 Rule 1 Example If the expected profit on each sale of Product X is $2000, what is the overall expected profit?

AP Statistics, Section 7.2, Part 16 Rule 1 Example A company believes that the sales of product Y is as follows. Y P(Y).4.5.1

AP Statistics, Section 7.2, Part 17 Rule 1 Example If the expected profit on each sale of Product Y is $3500, what is the overall expected profit?

AP Statistics, Section 7.2, Part 18 Rule 2 Example What is the total expected profits combined of both Product X and Product Y?

AP Statistics, Section 7.2, Part 19 Rules for Variances of Independent Distributions Only if the distributions are independent can you apply these rules… Rule 1: If a scale change involves a multiplier b, the variance changes by the square of b. Rule 2: The variance of sum of the two distributions is equal to the sum of the variances. Rule 2b: The variance of difference of the two distributions is equal to the sum of the variances.

AP Statistics, Section 7.2, Part 110 Example The Daily 3 lottery has the following mean and variance for its payout: What is the mean and variance of the winnings?

AP Statistics, Section 7.2, Part 111 Example The Daily 3 lottery has the following mean and variance for its payout: What is the mean and variance of the payouts of playing twice?

AP Statistics, Section 7.2, Part 112 Example The Daily 3 lottery has the following mean and variance for its payout: What is the mean and variance of the payouts of playing every day of the year?

AP Statistics, Section 7.2, Part 113 General Rules for Variances Here are the rules if the events are not independent (ρ=population correlation) Rule 1: If a scale change involves a multiplier b, the variance changes by the square of b. Rule 2: The variance of sum of the two distributions is equal to the sum of the variances. Rule 2b: The variance of difference of the two distributions is equal to the sum of the variances.

AP Statistics, Section 7.2, Part 114 Assignment Exercises, section 7.2: all Exercises, chapter review: all