Mathematical concepts for computer science: random variables and stochastic processes

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Mathematical concepts for computer science
random variables and stochastic processes

• Gaurav Raina
• 2009

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Approximate teaching outline

• Course outline as per guidelines
  http//www.cse.iitm.ac.in/academics/cs603.php
• Random Variables and Stochastic Processes
• Random variables, Functions of random variables,
  Sequences of random variables, Stochastic
  processes, Markov chains, Markov processes and
  Queuing theory
• Teaching approximately 4 weeks
• 1 week in August
• 1 week in September
• 2 weeks in November

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Approximate outline of material

• Random variables (approx 2 weeks)
• Basic concepts
• Axiomatic probability
• Examples class / Tutorial
• Discrete random variables
• Continuous random variables
• Examples class / Tutorial
• Stochastic processes (cover at least one topic)
• Markov Chains
• Markov processes
• Poisson processes

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Basic concepts

• Sample spaces
• Classical probability
• Combinatorial analysis
• Sampling models
• Sampling with replacement and with ordering
• Sampling without replacement and with ordering
• Sampling without replacement and without ordering
• Sampling with replacement and without ordering

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Axiomatic probability

• The axioms
• Booles inequality
• Inclusion-exclusion formula
• Bonferronis inequalities
• Conditional probability
• Multiplication rule
• Law of total probability
• Bayes theorem
• Independence
• Distributions

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Discrete random variables

• Introduction
• Expectation, variance and covariance
• Independence
• Conditional distributions

7
Continuous random variables

• Introduction
• Expectation, variance and
• standard distributions