MATH 380

Checklist  for  Exam I,   October 6,  2003


1.      Counting:
        -"splitting" a counting problem into "elementary" ones
        - recognizing the elementary problems as  "standard patterns"  
        (permutations,  combinations,  partitions, ...)

2.      Calculating probabilities via counting using the  "equally likely outcomes"  model.  
        (Poker,  bridge,  dice etc.  problems.)

3.      Recognizing data in the problem as statements about conditional probabilities  
        (hint: always NAME the events involved);  calculating conditional probabilities.  
        Conversely,  calculating probabilities from information about conditional probabilities.

4.      The Bayes' Formula,  applications.

5.      Independent events:
        - how to figure out whether two (or more) events are independent or not
        - using independence for calculating probabilities

6.      Random variables  
        (always ask yourself what is the set of possible values of the random variable)
        - finding cumulative distribution function,  probability mass function for a random variable
        - conversely,  obtaining qualitative and quantitative information about the random variable 
        from its  c.d.f.  and/or  p.m.f.

7.      Binomial random variables:  recognizing them and calculating related probabilities.

8.      Same for Poisson approximation to the binomial.