Statistics 7.2.2 by z8OBCl

VIEWS: 0 PAGES: 13

									Section 7.2.2
Means and Variances
of Random Variables
AP Statistics
www.toddfadoir.com/apstats
AP Statistics, Section 7.2, Part 1   2
Rules for Means
   Rule 1: The same scale
    change of elements of a
    probability distribution
    has the same effect on
                                          a bX  a  b X
                                           X Y   X  Y
    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 1   3
Rule 1 Example
   A company believes that the sales of
    product X is as follows.

      X         1000             3000                       5000   10,000

    P(X)          .1                 .3                      .4      .2

     X  1000  .1  3000  .3  5000  .4  10000  .2
                     X  5000 units
                       AP Statistics, Section 7.2, Part 1                   4
Rule 1 Example
   If the expected profit on each sale of
    Product X is $2000, what is the overall
    expected profit?
      X  1000  .1  3000  .3  5000  .4  10000  .2
                      X  5000 units

        0 2000 X  0  2000 X  10, 000, 000

                      AP Statistics, Section 7.2, Part 1    5
Rule 1 Example
   A company believes that the sales of
    product Y is as follows.

     Y         300               500                      750

    P(Y)        .4                 .5                     .1

           Y  300  .4  500  .5  750  .1
                  Y  445 units
                     AP Statistics, Section 7.2, Part 1         6
Rule 1 Example
   If the expected profit on each sale of
    Product Y is $3500, what is the overall
    expected profit?
            Y  300  .4  500  .5  750  .1
                  Y  445 units

        03500Y  0  3500Y  1,557,500

                    AP Statistics, Section 7.2, Part 1   7
Rule 2 Example
   What is the total expected profits
    combined of both Product X and
    Product Y?
               2000 X  10,000,000
                 3500Y  1,557,500
       2000 X 3500Y  10, 000, 000  1,575,500
                    11,557,500
                     AP Statistics, Section 7.2, Part 1   8
Rules for Variances of Independent
Distributions
   Only if the distributions are
    independent can you apply
    these rules…
   Rule 1: If a scale change                                   2
                                                                 a  bX   b 
                                                                            2    2
                                                                                 X
    involves a multiplier b, the
    variance changes by the
    square of b.                                          X Y   X   Y2
                                                           2        2

   Rule 2: The variance of sum of
    the two distributions is equal to                     X Y   X   Y
                                                           2        2     2
    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 1                       9
Example
   The Daily 3 lottery                                 X  .50
    has the following                                249.75
                                                       2
                                                       X
    mean and variance
    for its payout:                                 X  15.80
   What is the mean and
                                                        X 1  .50
    variance of the
    winnings?                                        249.75
                                                       2
                                                       X 1

                                                    X 1  15.80

                  AP Statistics, Section 7.2, Part 1                   10
Example
   The Daily 3 lottery                                 X  .50
    has the following                                249.75
                                                       2
                                                       X
    mean and variance
    for its payout:                                 X  15.80
   What is the mean and                 X  X  .50  .50  1.00
    variance of the
    payouts of playing                 X  X  249.75  249.75
                                        2

    twice?
                                                    X  X  22.34

                  AP Statistics, Section 7.2, Part 1                 11
Example
   The Daily 3 lottery                     X  .50
    has the following
    mean and variance                   X  249.75
                                           2

    for its payout:                       X  15.80
   What is the mean and
    variance of the
    payouts of playing        X  X   X  .50  365  182.5
    every day of the     X  X  X  249.75  365  91158.75
                          2

    year?
                                     X  X  X  301.92

                      AP Statistics, Section 7.2, Part 1   12
Assignment
 Exercises, section 7.2: 7.34-7.48 all
 Exercises, chapter review: 7.54-7.68 all




                AP Statistics, Section 7.2, Part 1   14

								
To top