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MA387 , MA391 Statistics
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Introduction to probability theory: probability spaces, properties of probabilities,
conditional probability, independence
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Combinatorial analysis and counting
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Random variables: discrete and continuous variables; expectation, variance,
covariance, moments
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The Markov, Cauchy-Schwartz-Bunjakowski, and Chebysev's Inequality; correletion
coefficients
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Jointly distributed random variables, marginal and conditional densities,
iterated expectation
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Distributions of sums, products, and quotients of random variables
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Order statistics, sampling statistics
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Moment generating functions, and characteristic functions, the Uniqueness
and Continuity Theorems
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The Weak Law of Large Numbers, the Central Limit Theorem, the normal and
Poisson approximations to the binomial density
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Relations between the normal, Chi Squared, Tau, and F densities,
and applications to sampling
Texts
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H.J. Larson, "Introduction to Probability" (Addison Wesley)
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Hogg & Craig . "Introduction to Mathematical Statistics" (Pentice Hall)
References
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P. Brémaud, "An Introduction to Probabilistic Modelling" (Springer)
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K.L. Chung, "Elementary Probability Theory with Stochastic Processes" (Springer)
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W. Feller, "An Introduction to Probability Theory and its Applications,
Vol I" (Wiley)
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P.G. Hoel, S.C. Port & C.J. Stone, "Introduction to Probability Theory"
(Houghton Mifflin)
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R.V. Hogg & A.T. Craig "Introduction to Mathematical Statistics" (Collier
Macmillan)
Back to 4th Year Syllabus
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