University of Hyderabad Logo School of Mathematics and Statistics University of Hyderabad

Programmes → Foundation course for M.Sc. in Mathematics/Applied Mathematics and I.M.Sc. in Mathematical Sciences

← Back to Courses

Foundation Course-Elements of Probability and Statistics

Course Code: FN 134; MA 304; MM 404  |  Credits: 3  |  Prerequisite: None

Syllabus Details

  • Unit I:(Random Experiments) Random experiments, sample spaces, sets, events and algebras; elements of counting — permutations and combinations.
  • Unit II:(Probability Measures) Axiomatic definition of a probability measure, with examples including the classical definition for finite sample spaces; properties of a probability measure and the theorem of total probability; conditional probability and Bayes’ theorem; independence of events and conditional independence.
  • Unit III:(Random Variables) Definition of a real valued random variable, its distribution function and the properties of that function; discrete and continuous random variables; existence of moments, probability and moment generating functions; Chebyshev’s inequality.
  • Unit IV:(Standard Distributions) Bernoulli, binomial, Poisson, geometric, negative binomial and hypergeometric random variables; uniform, normal, exponential, gamma and beta random variables; their distributions, moments and generating functions.
  • Unit V:(Joint Behaviour and Limits) Independence of random variables; limiting distributions; distributions of functions of random variables; joint distributions of discrete random variables, marginal and conditional distributions, conditional expectation and variance.
  • Unit VI:(Data Work) Different kinds of variables and how such data are displayed; frequency curves, empirical measures of location and spread; data on two or more variables — scatter plots and the correlation coefficient; fitting of distributions.

Course Learning Objective

  1. Identify uncertainty in nature and in other phenomena and processes.
  2. Recognize different random variables in nature and other phenomena, and identify their parameters.
  3. Write the sample space for any random experiment.
  4. Determine probabilities of events and probability distributions of random variables.
  5. Determine whether moments exist for a given random variable and, if so, compute them.
  6. Use probability generating and moment generating functions to study distributions of functions of random variables.
  7. Determine what data can tell us, and when anything more can be said on the basis of it.
  1. Feller, William. An Introduction to Probability Theory and its Applications. 3rd ed. Wiley Eastern, 1978
  2. Ross, Sheldon. A First Course in Probability. 6th ed. Pearson Education, 2007
  3. Prakasa Rao, B. L. S. A First Course in Probability and Statistics. World Scientific, 2009
  4. Moore, David S., Notz, William I. and Fligner, Michael A. The Basic Practice of Statistics. W. H. Freeman, 1994
← Back to Courses