\magnification=\magstep1
\centerline{Mathematics 375 -- Probability and Statistics I}
\centerline{Review Sheet, Final Exam}
\centerline{December 8, 2003}
\bigskip
\noindent
{\it General Information}
\bigskip
The final examination for this course will be given at 
2:30 a.m. on Thursday, December 18 in our regular class room,
Swords 302.
The exam will be roughly twice the length of one of the three
midterms, but you will have the full three hour period from
8:30 am to 11:30 am to work on it if you need that much time.
Like the second midterm, this will be an open book, open
notes exam.  Even more so than on that exam, of course,
it will be necessary to prepare carefully even so; you 
do not want to be flipping through the book for
every formula you need or similar examples to help you
get started on every problem.  There will not be enough
time to complete the exam if you are doing that.
\bigskip
\noindent
{\it Topics to be Covered}
\bigskip
\item{1)}  Descriptive statistics such as the mean, 
standard deviation, frequency histograms, etc.  The
``empirical rule''.
\item{2)}  Discrete sample spaces and counting techniques
(especially in connection with the ``sample point method''
for the probability of an event):  the $m\times n$ rule, permutations, 
binomial and multinomial coefficients.
\item{3)}  The ``event composition method'' for 
probabilities
\item{4)}  Conditional probabilities, independence of
events, Bayes' Rule, the Law of Total Probability
\item{5)}  Discrete random variables: probability 
distribution functions, cumulative distribution
functions, expected values and variances of functions
of a discrete random variable, moment generating 
functions.  Know the situations leading to 
binomial, geometric, Poisson, and hypergeometric random
variables and how to apply them.    
\item{6)}  Continuous random variables: probability 
distribution functions, cumulative distribution
functions, expected values and variances of functions
of a continuous random variable, moment generating 
functions.  Know the situations leading to uniform,
exponential, gamma, beta, and normal random
variables and how to apply them.   
\item{7)} Tchebysheff's Theorem.
\item{8)}  Multivariate probability distributions:
joint densities, marginal and conditional densities,
expected values in this setting, conditions for 
independence, the covariance and 
the general formula for the variance of a linear
combination of random variables.    
\bigskip
\noindent
{\it Suggestions on How to Study}
\bigskip
Start by reading the above list of topics carefully.
If there are terms there that are unfamiliar or for which
you cannot give the precise definition, {\it learn the definitions
now; memorize them if you have to!}  You simply cannot answer
a question about this material if you do not know what the 
terms mean.  Review the class notes.  {\it Everything on 
the final will be similar to something we have discussed at
some point this semester.}  Also look back over your graded
problem sets and exams.  If there are problems that you 
did not get the first time around, try them again now.  Then
go through the suggested problems from the three
review sheets.  If you have worked these out previously,
it is not necessary to do them all again.  But try a representative
sample ``from scratch'' -- don't just look over your old
solutions and nod your head if it looks familiar.  You
need the practice thinking through the logic of how
the solution is derived again!
\bigskip
\noindent
{\it Suggested Review Problems}
\bigskip
Look at the problems from the two previous
review sheets for the topics from Chapters 1 - 4.
From Chapter 5/11,27,28,57,58,59,61,84,96,120,121,122,123,125,133,134
\bigskip\noindent
{\it Review Session}
\bigskip
I will be happy to run a review session for the final
exam during study week.  We can discuss a time in class
on Monday, December 8.
\bye

