Mathematics 2Y Spring 1995
Probability Theory
Contents
x1. Basic concepts. Sample space, events, inclusion-exclusion principle,probabilities. Examples.
x2. Independence, conditioning, Baye's formula, law of total probability.Examples.
x3. Discrete random variables. Expectation, variance, independence.Binomial, geometric and Poisson distributions and their relationships. Examples.
x4. Probability generating functions. Compound randomness. Applications.
x5. Continuous random variables. Distribution functions, density functions.Uniform, exponential and normal distributions.
x6. Moment generating functions. Statement of Central Limit Theorem.Chebyshev's inequality and applications (including the weak law of large numbers).
x7. Markov chains. Transition matrix, steady-state probability vectors,regularity, an ergodic theorem.
x8. Birth and Death processes. Steady states. Application to telecom circuits. M/M/1 queue.If there is time we will go on to discuss reliability. Examples on the problem sheets will include some ideas associated with simulation.