Introduction to Probability (with examples using R)

Overview

The course will cover basic concepts in Probability. It will begin with fundamental notions of Sample Space, Events, Probability, conditional probabilities And independence. We shall formalise notation in terms of Random Variables and discuss standard distributions such as (discrete) Uniform, Binomial, Poisson, Geometric, Hypergeometric, Negative Binomial and (continuous) Normal, Exponential, Gamma, Beta, Chi-square, and Cauchy. We will conclude with the law of large numbers and central limit theorem. A unique feature of this course will be that we will use the package R to illustrate examples.
INTENDED AUDIENCE :Anyone who has completed one year of undergraduate degree in Engineering or Sciences PREREQUISITES : Basic CalculusINDUSTRIES SUPPORT :None

Syllabus

COURSE LAYOUT

Week 1: * Sample Space, Events and Probability * Conditional Probability and IndependenceWeek 2: * Independence and Bernoulli Trials * Poisson ApproximationWeek 3: * Sampling without Replacement * Discrete Random VariablesWeek 4: * Discrete Random Variables: o Distribution, Probability Mass function o Joint, Marginal, and Conditional o IndependenceWeek 5: * Discrete Random Variables o Expectation and Variance o Correlation and CovarianceWeek 6: * Markov and Chebyschev Inequalties * Conditional Expectation, Conditional VarianceWeek 7: * Uncountable Sample Spaces * Probability Densities * Continuous Random Variables: Uniform DistributionWeek 8: * Exponential Random and Normal Random Variable * Joint Density, Marginal and Conditional DensityWeek 9: * Independence * Functions of Random VariablesWeek 10: * Sums of Independent Random variables * Distributions of Quotients of Independent Random variables.Week 11: * Law of Large Numbers (without Proof)Week 12: * Central Limit Theorem (without Proof)