Introduction to Probability and Stochastic Processes | 1 | Papoulis (2002), Krishnan (2006) | |

Set Theory | 2 | do. | |

Relations, Functions, Probability | 3 | do. | |

Probability Experiments: Repeated, Dependent, Cascaded | 4 | do. | |

Joint Probability, Conditional Probability, Total Probability | 5 | do. | |

Combinatronics, Birthday Problem, Bayes Rule | 6 | do. | |

Bayes Rule Application, Partitioned Footpath, Partioned Floor, Trains on a Junction | 7 | do. | |

Trains on a Junction, A local bus stop, Random line partition | 8 | do. | |

Equally likely outcomes, Random Variables, Chuk-a-luck, Binomial & Poisson Distributions | 9 | do. | |

CDF of Poisson PMF, Joint Distribution Example, Marginal PMF | 10 | do. | |

Conditional Distribution, Conditional PMF, Expected Value, Transformation of Random Variables | 11 | do. | |

Transformation of RVs, Conditional Expectation, Co-variance and Correlation | 12 | do. | |

Continuous Random Variable, Probability Density Function, PDF and CDF of a Continuous RV | 13 | do. | |

CDF of a Continuous RV, CDF and PDF of Nozzle Height, Exponential RV | 14 | do. | |

Failure of TV Set Example, Gaussian RV | 15 | do. | |

Mean of Transformed RV, Height Distribution of Humans Example, Higher Moments | 16 | do. | |

Scaling of Gaussian RV, Standard Gaussian Events, Joint Distributions, Pair of RVs | 17 | do. | |

Pair of RVs , Buffon's Needle, Exponential RV Pair, Pair of Erlang RVs | 18 | do. | |

Exponential RV Pair, Pair of Dependent RVs, Correlation & Covariance | 19 | do. | |

Correlation & Covariance, Correlated Gaussian RVs | 20 | do. | |

Function of two RVs, Evaluation of Fz(Z), CDF & PDF of Z = X + Y | 21 | do. | |

Function of two RVs, Evaluation of Fz(Z), CDF & PDF of Z = Y / X, CDF & PDF of Z = max (X, Y) | 22 | do. | |

Multiple derived RVs, Probability Computation | 23 | do. | |

Pair of derived RVs | 24 | do. | |

Direct Computation of Derived CDF | 25 | do. | |

Non-invertible Transformations | 26 | do. | |

Moments of U and V from f(x, y) | 27 | do. | |

Expectation of Transformed Random Variables, Covariance Matrix, Eigenvalues & Eigenvectors | 28 | do. | |

Vector RVs, Transforming Vector RVs | 29 | do. | |

PDF of Z = X+X ? 2X, Characteristic Functions | 30 | do. | |

Convergence of Sequence, Convergence of RVs | 31 | do. | |

Norm of Vectors and Function, Convergence of RVs, Inequalities | 32 | do. | |

Basics of Markov chains, Examples of Markov chains | 33 | Lawler (2006) | |

Transition probabilities, Stochastic matrix, Stationary probability distribution | 34 | do. | |

Periodic and aperiodic Markov chains, Multivariate joint probability | 35 | do. | |

Transient and recurrent Markov chains, Return times of recurrent states | 36 | do. | |

n-step stochastic matrix, n-step reachability | 37 | do. | |

Diagonalization of stochastic matrix, Periodic and aperiodic recurrence | 38 | do. | |

Eigen-analysis of stochastic matrix | 39 | do. | |

Bipartite and tripartite graphs of Markov chains | 40 | do. | |

Asymptotic behaviour of Markov chains | 41 | do. | |

Partitioning of Markov chains | 42 | do. | |

Markov chains with infinite state space | 43 | do. | |

Random walk on real line, Random walk on 2-d plane, Random walk in higher dimensions, Continuous-time Markov chains | 44 | do. | |

Continuous-time Markov chains, Poisson arrival and departure processes, Stationary probability distribution, Queuing theory | 45 | do. | |