### MA261 STATISTICAL AND NUMERICAL TECHNIQUES

Title of the unit | Minimum number of hours | |
---|---|---|

1 | Sampling Distributions and Test of Hypotheses | 12 |

2 | Simulation | 12 |

3 | Simple Regression and Simple Correlation | 06 |

4 | Interpolation and Curve Fitting | 15 |

5 | Numerical Integration, Solution of Different Types of Equations | 15 |

Unit No. | Topics | Teaching Hours |
---|---|---|

1 | Sampling Distributions and Test of Hypotheses:1.1 Population and sample, function of random variables associated with normal Distribution, Central limit theorem. 1.2 Random sampling, Sample moments and their distributions: Chi-square, t and F distributions. 1.3 Point estimation and interval estimation: Estimation of population mean, population variance, population proportion, one population and two populations. 1.4 Introduction to hypothesis Testing, z- test, t-test, chi-square test and F-test, one sample and two samples tests |
12 |

2 | Simulation:2.1 Introduction to random numbers. 2.2 Generating random numbers from probability distributions: Binomial, Poisson, Uniform, Exponential and Normal. 2.3 Variance reduction techniques. 2.4 Markov Chain, Monte Carlo Method and its applications. |
12 |

3 | Simple Regression and Simple Correlation:3.1 Measure of association between two variables. Types of correlation, Karl Pearson’s Coefficient of correlation and its mathematical properties. 3.2 Spearman’s Rank correlation and its interpretations. 3.3 Regression Analysis: Concept and difference between correlation and regression, linear regression equations, properties of regression coefficients. |
06 |

4 | Interpolation and Curve fitting:4.1 Errors in numerical analysis: types of errors, sources of errors. 4.2 Interpolation, Lagrange’s interpolation formula. Newton’s divided difference table and Newton’s Interpolation polynomial. 4.3 Finite differences and associated operators. 4.4 Newton’s forward interpolation formula, Newton’s backward interpolation formula. 4.5 Least squares curve fitting methods, linear and quadratic curve fitting. |
15 |

5 | Numerical Integration and Numerical Solution of Different Types of Equations:5.1 Numerical Integration: Rectangle rule, trapezoidal rule and Simpson’s rules (1/3 and 3/8) and their composite rules. 5.2 Numerical solution of equations: Bisection method, False position (Regula-Falsi) and Newton-Raphson method. 5.3 Numerical solution of system of simultaneous linear equations: Gauss Jacobi Method and Gauss Seidel Method. 5.4 Numerical Solution of Ordinary Differential Equations: Taylor’s series, Euler’s, and Runge- Kutta (2nd and 4th order) methods. |
15 |