1. MathematicalMarketing Slide 4b.1 Distributions Chapter 4: Part b – The Multivariate Normal Distribution We will be discussing  The Multivariate Normal Distribution  Other Distributions (These topics are needed for Chapters 5)

2. MathematicalMarketing Slide 4b.2 Distributions The Multivariate Normal Function According to the multivariate density function, the probability that the random vector x = [x 1 x 2 ··· x p ]′ takes on a particular set of values is given by The analogous distribution function is given by

3. MathematicalMarketing Slide 4b.3 Distributions Bivariate Normal with Three Values of   = 0.0  = 0.4  = 0.6

4. MathematicalMarketing Slide 4b.4 Distributions The  2 Distribution The Chi Square Is a Sum of Squared Z scores: Pr(  2 ) It approaches normality as df gets large:

5. MathematicalMarketing Slide 4b.5 Distributions Student’s t Distribution The t is analogous to the normal but with  2 unknown. It approaches normality also as the df gets large.

6. MathematicalMarketing Slide 4b.6 Distributions The F Distribution The F is a ratio of Chi Squares. The t is an F 2 with 1 df in the numerator.