Syllabus  MA387/MA391
MA387 , MA391 Statistics

Introduction to probability theory: probability spaces, properties of probabilities,
conditional probability, independence

Combinatorial analysis and counting

Random variables: discrete and continuous variables; expectation, variance,
covariance, moments

The Markov, CauchySchwartzBunjakowski, and Chebysev's Inequality; correletion
coefficients

Jointly distributed random variables, marginal and conditional densities,
iterated expectation

Distributions of sums, products, and quotients of random variables

Order statistics, sampling statistics

Moment generating functions, and characteristic functions, the Uniqueness
and Continuity Theorems

The Weak Law of Large Numbers, the Central Limit Theorem, the normal and
Poisson approximations to the binomial density

Relations between the normal, Chi Squared, Tau, and F densities,
and applications to sampling
Texts

H.J. Larson, "Introduction to Probability" (Addison Wesley)

Hogg & Craig . "Introduction to Mathematical Statistics" (Pentice Hall)
References

P. Brémaud, "An Introduction to Probabilistic Modelling" (Springer)

K.L. Chung, "Elementary Probability Theory with Stochastic Processes" (Springer)

W. Feller, "An Introduction to Probability Theory and its Applications,
Vol I" (Wiley)

P.G. Hoel, S.C. Port & C.J. Stone, "Introduction to Probability Theory"
(Houghton Mifflin)

R.V. Hogg & A.T. Craig "Introduction to Mathematical Statistics" (Collier
Macmillan)
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