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The topics
of this exam are included in the courses Probability Theory ESMA-6600,
and Statistical Methods, ESMA-6305.
Topics in
Probability:
·
Sample
spaces and events.
·
Definition
of probability, conditional probability, and independent events.
·
Expected
value and variance of a random variable.
·
Distributions
of discrete random variables: Binomial, Geometric, Poisson.
·
Distributions
of continuous random variables: Uniform, exponential, Normal.
·
Distribution
of function of random variables.
·
Moment
generating function.
·
Bi-dimensional
random variables, joint distributions, marginal distributions,
conditional distributions.
·
Limit
Theorems.
Topics in Statistical Methods:
·
Review of distribution
of random variables: Binomial, Poison, Multinomial.
·
Sampling
distributions: t-student, Chi-square, F.
·
Inference
based on one-sample: Confidence intervals and hypothesis testing.
·
Inference
based on two-sample: confidence intervals and hypothesis tesing.
·
Analysis of
contingency tables.
·
Correlation.
·
Linear
Regression.
·
Experimental
designs: One-way analysis of variance, two-way analysis of variance,
multiple comparisons.
·
Multiple
linear regression and correlation.
Bibliography (Probability part):
·
Modern Mathematical Statistics, E.J. Dudewicz and S.N. Mishra. (1988) John Wiley, NY.
·
Probability, W. Feller. (1978) Vol. I.
John Wiley, NY.
·
Probability Theory, R.G. Laha. (1976). John Wiley, NY.
·
An Introduction to Probability Models, S.
Ross. (2002). 8th Ed.
Academic , Boston
·
A first course in probability, S.
Ross. (2001). Sixth edition Prentice Hall.
Bibliography
(Statistical Methods part):
·
Statistical Methods of Analysis, Chin
Long Chian, (2003) Word Scientific
Publishing.
·
Statistics for Research, S. Dowdy, S.Waerden and S. Chiko, 3rd Ed, John
Wiley, NY.
·
Modern Applied Statistics with S-plus, B. Venables and B.D.R. Ripley, Springer-Verlag.
·
Statistics for Applied Solving Problems and Decision Making, R.
Larsen, M. Marx and B. Cooli, Duxbury Press, Boston, 1997.
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