STAT  314
CHAPTER 3:  PROBABILITY

HOMEWORK/ASSIGNMENTS

Read pp 91-136 in Chapter 3;
read case studies on p. 100, p. 126, and p. 136.
Review Key Terms and Key Formulas p. 138
Work exercises

KEY TERMS & TOPICS

* "Probability permits us to make the inferential jump from sample to
population and then to give a measure of reliability for the inference."

* an experiment is an act or process of observation that leads to a
single outcome (that typically cannot be predicted with certainty)

* a sample point is the most basic outcome of an experiment

* the sample space is the set of all its sample points

* probability rules for sample points:all sample point probabilities are
  between 0 and 1; probabilities of all the sample points must sum to 1

*  a Venn diagram is a useful graphical representation of a sample space
and events

* an event is a specific collection of sample points

* the probability of an event A is calculated by summing the
probabilities of the sample points in A

* compound events
  union of events : A U B
  intersection of events: AB

* complement of event A

* "additive" rule of probability: P(A U B)=P(A)+P(B)-P(AB)

*  mutually exclusive events have no sample points in common

* conditional probability:    P(A|B)=P(AB)/P(B)

* multiplicative rule of probability:  P(AB)=P(A) P(B|A)

* tree diagram

* A and B are independent events iff P(A|B)=P(A) and P(B|A)=P(B)

* A and B are independent events iff P(AB)= P(A)P(B)

* Bayes' rule:         P(A|B)=P(B|A)P(A)/[P(B|A)P(A)+P(B|~A)P(~A)

* a (simple) random sample of size n from a population is a sample
selected in such a way that every set of n elements in the population
has an equal probability of being selected

* random number generator

* the combinatorial quantity "N choose n" = N!/[n!(N-n)!]

* if population is of size N,  there are "N choose n" samples of
size n

* 3 interpretations or approaches to probability:
      relative frequency;
      subjective assessment; and
      equally-likely outcomes


* probability axioms:
   1)  P(E)>=0 for any event E
   2)  P(S)=1 where S is the sample space
   3)  If A equals the union of disjoint events E1, E2, ...,
       then P[A]=sum{P(Ei)}

* Introductory combinatorics

* fundamental counting principle:  k-step process, ni ways for step i:
  n1 x n2 x...x nk ways to do process

* number of permutations (ordered subsets):  nPr=n!/(n-r)!

* number of combinations (subsets): nCr= n!/[(n-r)!r!]

* number of "words"

* inclusion/exclusion principle