Probability Theory: Elementary concepts on probability – axiomatic definition of probability –conditional probability – Bayes’ theorem – random variables – standard discrete and continuous distributions – moments of random variables – moment generating functions – multivariate randomvariables – joint distributions of random variables – conditional and marginal distributions – conditional expectation – distributions of functions of random variables – t and χ2 distributions – Schwartz and Chebyshev inequalities – weak law of large numbers for finite variance case – central limit theorem for iid finite variance case.
Statistics: Elementary concepts on populations, samples, statistics – sampling distributions of sample mean and sample variance – point estimators and its important properties – point estimator for mean and variance and proportion – confidence interval for sample mean – tests of hypotheses – Chi-squared test of goodness of fit.
Numerical Methods: Solution of algebraic and transcendental equations – system of linear algebraic equations – interpolation – numerical integration – numerical solution of ordinary differential equations – system of nonlinear algebraic equations.
Walpole, W. E., Myers, R. H., Myers, S. L., and Ye, K., Probability & Statistics for Engineers & Scientists, 9th ed., Pearson Education (2012).
2. Jain, M. K., Iyengar, S. R. K., and Jain, R. K., Numerical Methods for Scientific and Engineering Computation, 4th ed., New Age International (2005).
Johnson, R. A., Miller & Freund’s Probability and Statistics for Engineers, 6th ed., Prentice Hall (2000).
2. Milton, J. S. and Arnold, J. C., Introduction to Probability and Statistics: Principles and Applications for Engineering and the Computing Sciences, 4th ed., McGraw-Hill (2002).
3. Ross, S. M., Introduction to Probability and Statistics for Engineers and Scientists, 3rd ed., Academic Press (2004).
4. Hogg, R. V. and Tanis, E. A., Probability and Statistical Inference, 7th ed., Prentice Hall(2005).
5. Larsen, R. J. and Marx, M. L., An Introduction to Mathematical Statistics and Its Applications, 4th ed., Prentice Hall (2005).
6. Conte, S. D. and de Boor, C., Elementary Numerical Analysis, 3rd ed., TMH (2005).
7. Krishnamurthy, K. V., Numerical Algorithms, Affiliated East-West Press (1986).
Course Outcomes (COs):
CO1: Learn fundamental concepts of probability, statistics and numerical methods in detail to enable students to identify the relevance of these concepts and apply them in the modelling and performance analysis of several electronics and communication systems.
CO2: Understand random variables and their probability distributions chosen to model various random phenomena arising in models of systems.
CO3: Analyse sampling theory to understand the information in a sample to estimate system parameters.
CO4: Understand various standard numerical techniques to apply them appropriately in the modelling and analysis of several engineering systems.