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• 8:12 PM, Saturday, 16 Oct 2021

 Course Undergraduate Semester Sem. V Subject Code MA311 Subject Title Probability, Statistics, and Numerical Methods

##### Syllabus

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 random variables – joint distributions of random variables – conditional and marginal distributions – conditional expectation – distributions of functions of random variables – t and χ 2 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.

##### Text Books

1. Walpole, R. E., Myers, R. H., Myers, S. L., and Ye, K., Probability & Statistics for Engineers & Scientists , 9 th ed., Pearson Education (2012).

2. Jain, M. K., Iyengar, S. R. K., and Jain, R. K., Numerical Methods for Scientific and Engi- neering Computation , 4 th ed., New Age International (2005).

##### References

1. Johnson, R. A., Miller & Freund’s Probability and Statistics for Engineers , 6 th 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 , 4 th ed., McGraw-Hill (2002).

3. Ross, S. M., Introduction to Probability and Statistics for Engineers and Scientists , 3 rd ed., Academic Press (2004).

4. Hogg, R. V. and Tanis, E. A., Probability and Statistical Inference , 7 th ed., Prentice Hall (2005).

5. Larsen, R. J. and Marx, M. L., An Introduction to Mathematical Statistics and Its Applica- tions , 4 th ed., Prentice Hall (2005).

6. Conte, S. D. and de Boor, C., Elementary Numerical Analysis , 3 rd ed., TMH (2005).

7. Krishnamurthy, K. V., Numerical Algorithms , Affiliated East-West Press (1986)