Course Archives Theoretical Statistics and Mathematics Unit
Course: Probability Theory II
Time: Currently not offered
Syllabus
Past Exams

Syllabus:

i) Distribution of sum of two independent random variables. Functions of more than one discrete random variables. Markovs inequality, Tchebyshevs inequality and Weak law of large numbers.
ii) Generating functions, Fluctuations in coin tossing and random walks, Review of conditional distributions and random sums of random variables.
iii) Review of probability densities on the real line, Bivariate continuous distributions, bivariate CDFs, independence, distribution of sums, products and quotients for bivariate continuous distributions, Examples: Bivariate Dirichlet and bivariate normal distributions. Independence and marginal distributions. Distributions of functions of bivariate continuous random vectors.
iv) Conditional distribution, conditional density, examples. Conditional distributions of bivariate normal distribution.
v) Expectation of functions of random variables with densities, variance and moments of random variables. Conditional expectation and variance, illustrations.
vi) Discussion of a.s. convergence, convergence in probability and distribution. Statements of CLT and Strong law of large numbers for i.i.d. random variables.

Reference Texts:

(a) W. Feller: Introduction to Probability: Theory and Applications - Vol. I and II.
(b) J. Pitman: Probability.
(c) Sheldon Ross: Probability Models.
(d) Santosh S. Venkatesh: Theory of Probability - Explorations and Applications.
(e) P. G. Hoel, S. C. Port and C. J. Stones: Introduction to Probability Theory.
(f) K. L. Chung: Elementary Probability Theory with Stochastic Processes.
(g) R. Meester: A Natural Introduction to Probability Theory.

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Past Exams
Midterm
 23.pdf 24.pdf
Semestral
 22.pdf 23.pdf 24.pdf
Supplementary and Back Paper
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