Here are remarks on preparing for the first midterm exam. 

 I can only sample the things you 
should know. If you understood your homework 
and the lectures you should be in good shape. 

Know the axioms for a probability space. 
In particular, know that the all-important 
third axiom applies to a countable list 
of mutually exclusive events. 

Be able to solve for probabilities of unions 
or intersections of events, given other 
probabilities. 

Be able to count subsets ("n choose k") and 
compute likelihood of subsets with some 
probabilities as in the homework.  

Be able to use a tree diagram and  compute 
with conditional probability. There will be 
a problem involving reversed conditional 
probabilities.  
Be able to compute probabilities involving 
independent events.

Be able to make a histogram. 

Know the difference between  continuous and 
discrete random variables. (An rv is continuous 
if every output value has probability zero, 
and an rv is discrete if the set of possible 
output values is countable.) 

For a discrete random variable, be able to compute 
the expected value, standard deviation and variance.  


Know the intuition: 
--probability of an event is its likely long term 
  relative frequency in a series of many 
  independent experiments 
--expected value of an rv X is the likely long 
  term average of measurements using X, in a series 
  of many independent experiments 

Be able to compute the cdf and pmf for an rv. 

Understand how to compute probabilities involving 
sampling with and without replacement (as in the 
homework problems A,B).  

The online testbank has samples of my midterm 1 exams 
from Fall 2003, Fall 2000, Spring 99 and a summer session. 

Good luck.