Final Examination

The final examination is scheduled as follows:

• Date: Friday, November 30, 2018.
• Time: 9:00 am - 12:00 noon
• Venue: LH-1, Department of Mathematics, IISc

Syllabus etc

Please note the rules for the examination.

The syllabus includes all the material covered in the course. However, most of the weightage will be for topics in the second half of the course. A rough list of topics is below.

• Probablitity
  • Discrete Probability spaces; laws of Probability; combinations of Events.
  • Independence and Conditional Probabilities.
  • Discrete and Continuous distributions; some important distributions: Bernoulli, Binomial, Geometric, Exponential, Cauchy, Poisson.
  • Random variables: Distributions, Independence, Expectation and Variance; conditional distributions and conditional expectation.
• Markov Chains
  • Classification of States: accesibility, communicating classes, essential states, irreducibility.
  • Transience and recurrence; criteria for recurrence.
  • Null and positive recurrence; stationary distributions.
  • Random walks on integers and tuples of integers: symmetric and assymmetric.
• Poisson Process
  • Counting processes; charactrization of the Poisson process.
  • Associated distributions: Exponential, Poisson, Gamma.
  • Thinning and superposition.