Axioms of probability - Conditional probability - Total probability - Baye’s theorem- Discrete and continuous random variables – Moments – Moment generating functions and their properties.
Sampling distributions – Tests for single mean, proportion and difference of means (large and small samples) – Tests for single variance and equality of variances – Chi square test for goodness of fit – Independence of attributes.
Newton Raphson method – Solution of linear system of equations – Gauss elimination method – Pivoting Gauss Jordan methods – Iterative methods of Gauss Jacobi and Gauss Seidal.
Lagrange’s interpolation – Newton’s forward and backward difference interpolation – Approximation of derivatives using interpolation polynomials – Numerical single integration using Trapezoidal and Simpson’s 1/3 rules.
Single step methods: Taylor’s series method – Euler’s method – Modified Euler’s Method – Fourth order Runge-Kutta method for solving first order equations – Multi step methods: Milne’s predictor-corrector methods for solving first order equations.
Reference Book:
Walpole. R.E., Myers. R.H., Myers. S.L., and Ye. K., “Probability and Statistics for Engineers and Scientists”,9th Edition, Pearson Education, Asia, 2010. Burden, R.L and Faires, J.D, "Numerical Analysis", 9 th Edition, Cengage Learning, 2016. Devore. J.L., "Probability and Statistics for Engineering and the Sciences", Cengage Learning, New Delhi, 8 th Edition, 2014. Gerald. C.F. and Wheatley. P.O. "Applied Numerical Analysis" Pearson Education, Asia, New Delhi, 7th Edition, 2007. Spiegel,M.R., Schiller, J. and Srinivasan,R.A., "Schaum’s Outlines on Probability and Statistics”, Tata McGraw Hill edition, 4th Edition, 2012.
Text Book:
Johnson, R.A., Miller, I and Freund J., “Miller and Freund’s Probability and statistics for Engineers”, Pearson Education Asia, 9th Edition, 2018. Grewal, B.S and Grewal, J.S, “Numerical methods in Engineering and Science”, 10th Edition, Khanna Publishers, New Delhi, 2015
