Probability Axioms: rules 1 thru 4 on p. 305. ANY method
of assigning probabilities to sets must result in a system that obeys these.
Note: All the following obey axioms 1 thru 4: All
can be used as metaphors or models for probability models.
Area
(If area of whole space is 1), Volume (If volume of whole space is
1)
Weight
(If
weight of whole space is 1)
Proportion
(count
of items in set/ total count)
Because probability is about something "happening", a (decision) tree is sometimes a good model, especially for a situation when things happen in sequence. (More p. 354)
Independence (rule 5: Multiplication rule) is used here for :
(a) assuming independence when setting up a probability
model, and using the mult. rule to assign probabilities .
Later we'll use it to (b) check if two events
are independent in a known model, by seeing if the mult. rule holds.
Read 4.2 for this assignment. I am assuming this is familiar
to most people, so bring any questions about the reading or problems to
class! Note, the text uses (A and B) where you may be used to (A
intersect B), (A or B) where you may be used to (A union B).
For next class, read 4.3, Random variables.
| Hand in:
p. 306 4.11 likelihood 4.12 c, d, e, 4.13 a, b sample spaces 4.15, 17, 18, 20 probability assignments 4.24 farms--set notation. Note how we can change a population distribution into a probability mechanism by saying "choose an individual at random from the population. " 4.27 committee of 2 List them all--you should get 10. - - - - - - - - Independence p. 306 4.23 college/hsrank Assume, when choosing two individuals from a very large population, that having the first one already chosen has "no" effect on the population you draw the second from. Not quite true, but a good enough approximation (Note, if the population is very small, choosing one will affect the population left to draw from.). 4.28 battles 4.29 computer chips 4.33 dice sequence 4.30 multiplication OK? |
Read, discuss
I use 4.25 in class. Take a look at it. - - - - - - - - Independence 4.31 age/education table |
Optional
4.16, 19, 21, 22--more of the same. - - - - - - - - (Independence, more of the same) 4.32 Xmas lites |
| Sievers home | Math251-Fall01/DayP20.htm | 10/17/01 |