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Unformatted text preview: CountingCombinatorial analysis. Chapter 1(14).
• Random variables, discrete random variables, Ch 4(1,2)
• Expected value, variance, moment generating function Ch 4(35), Ch 7(7).
• Bernoulli, Binomial, Poisson, Geometric, Neg. Binomial, Hyper. Zipf Ch 4(68) Ch 7(7)
• Expected Value of Sums of Random Variables and Cum distribution properties Ch 4(910)
• Continuous random variables, Ch 5(13, 5) 4 •
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• The normal random variable. , gamma, Weibull, Beta, Pareto, Ch 5(4,6)
Distribution of a Function of a random variable. Cha 5(7)
Joint distribution of two random variables, marginals,Ch 6(12, 4, 5, )
Sums of independent random variables. Ch 6 ( 3)
Joint probability distributions of functions of random variables. Ch 6(7)
Properties of Expectations, sums. Ch 7(12)
Moments of number of events that occur. Ch 7(3),
Covariance, Variance of Sums and Correlations. Ch 7(4)
Conditional expectations. Ch 7(56)
Moment generating functions Ch 7(7) (They will be introduced earlier in each chapter on distributions)
Bivariate Normal Distributions, general definition of expect Ch 7(8)
Markov, Chevyshev and Weak Law of Large Numbers, Ch 8(12)
The Central Limit Theorem. Ch. 8(3)
Strong Law of Large Numbers and other inequalities. Ch 8(45) VIII. R and other software resources.
• http://www.ats.ucla.edu/stat/r/ This is our own UCLA ATS R resource page. They have consulting hours as
well. Check http://www.ats.ucla.edu/stat/
• http://cran.rproject.org/doc/manuals/Rintro.pdf (chapter 8)
• The UCLA Consulting Center also has a schedule and consultants that answer R questions:
http://scc.stat.ucla.edu/officehours/ It also has online resources
• You are not required to learn R on your own. We will guide you and tell you what you need for each
simulation. But after we teach you, you will be given some commands that will be practiced in front of you
and you are expected to repeat on your own after you have seen them. Students in past classes have found
that using simulations has helped them understand and like probability more. So investing some time in
accessing and familiarizing yourself with R is a great investment. The ATS web site given above has
simple modules to start getting familiar with the interface. R is available in Powell CLICC labs and most
labs on campus. It is also available in the laptops that you may check out from the libraries. Downloading it,
if you have a computer, would make it very easy for you to use it.
• Applets are also useful to see some concepts in Probability. You may want to explore
http://socr.stat.ucla.edu/ 5...
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This document was uploaded on 02/02/2014.
 Winter '14

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