Math-IIIB (Introductory Probability and Statistics)

Course Code: MM 203 | Credits: 3 | Prerequisite: Basic Mathematics at high school level

Unit I:(Probability) Random experiments, sample spaces and events; the probability measure on events — definition, properties and examples; conditional probability, Bayes’ theorem and independent events.
Unit II:(Random Variables) Definition of a random variable; the standard discrete and continuous random variables — Bernoulli, binomial, geometric, Poisson, exponential, gamma and normal; expectation, variance and other properties.
Unit III:(Bivariate Distributions) Bivariate random variables, joint distributions, covariance and correlation between two random variables, independence and distributions of sums.
Unit IV:(Data Analysis) Data collection methods and types of data; graphical summaries; numerical summaries of univariate data; bivariate summaries and measures of association.
Unit V:(Statistical Inference) Introduction to statistical inference, population parameters, variables of interest, statistics and estimators as random variables.

Identify uncertainty in nature and in other phenomena and processes.
Recognize different random variables in nature and other phenomena, and identify their parameters.
Write the sample space for any random experiment.
Determine probabilities of events and probability distributions of random variables.
Determine the moments of widely known distributions.
Determine what data can tell us, and when anything more can be said on the basis of it.
Identify the concepts of statistical inference: parameter, statistic, estimator, estimate and pivotal quantity.

Ross, Sheldon. A First Course in Probability. 6th ed. Pearson Education, 2007
Ramachandran, K. M. and Tsokos, Chris P. Mathematical Statistics with Applications. Academic Press, 2009
Daniel, Wayne W. Biostatistics: A Foundation for Analysis in the Health Sciences. 9th ed. Wiley, 2008
Moore, David S. The Basic Practice of Statistics. W. H. Freeman, 2003