MATH 380

Checklist  for  Final Exam,   December 10,  2003, 8:30-11:30 a.m., Yost 104


1. 	Counting:
	-"splitting" a counting problem into "elementary" ones
	- recognizing the elementary problems as  "standard patterns"  
	(permutations,  combinations,  partitions, ...)
	-calculating probabilities via counting using the  "equally likely outcomes"  model.  
	(poker,  bridge,  dice etc.  problems.)

2.  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.
	The Bayes' Formula,  applications.

3.  Independence:
	- the "common sense" meaning of independence of events or random variables;  
	recognizing independence in "word problems"
	- how to figure out MATHEMATICALLY whether two (or more) events or random variables are 
	independent or not
	- using independence for calculating probabilities, expectations, variances ...

4.  Random variables:  
	(always ask yourself what is the set of possible values of the random variable)
	- finding cumulative distribution function,  probability mass function, density etc.
	for a random variable described in other terms
	- obtaining qualitative and quantitative information about the random variable 
	from its  c.d.f.  and/or  mass or density function;  this includes calculating 
	probabilities, expectations,  variances ...
        

5.  Standard random variables:  
	Bernoulli, binomial, Poisson, geometric, negative binomial, uniform, normal, 
	exponential, Gamma.  
	Recognizing them from the context and calculating related probabilities and such.
	It is necessary to know their densities/mass/c.d. functions. Should know the formulae 
	expectations and variances in terms of the parameters.  
	Should know how to figure out normal probabilities using tables or calculators.
	Should know rules for adding independent random variables of the same type.


6.  Normal and Poisson approximation to the binomial;  knowing when they are appropriate.  
	Central Limit Theorem.


7.	Joint mass/density functions, marginal mass/density functions, the role of independence.  
	Calculating the same as in 3 and 4 in this context.  
	Covariance and correlation. 
		
		
You are allowed  a  full page (8.5 x 11,  one-sided)   "formula  sheet".  
Normal probabilities table and a table of integrals will be provided.
It is recommended that you bring calculators.