| MAFC-311 Probability Statistical and Numerical Techniques | |||||||
|---|---|---|---|---|---|---|---|
| Teaching Scheme | Credit | Marks Distribution | Duration of End Semester Examination | ||||
| L | T | P | Internal Assessment | End Semester Examination | Total | ||
| 3 | 1 | 0 | 4 | Maximum Marks: 40 | Maximum Marks: 60 | 100 | 3 Hours |
| Minimum Marks: 16 | Minimum Marks: 24 | 40 | |||||
Unit-I
Probability Theory: Counting principles, probability axioms, sample space and events, conditional probability & Baye’s Theorem. Random variable, discrete & continuous probability distribution, expectation, variance, standard deviation. Joint probability distribution, mass function, distribution function, marginal distribution function, covariance.
Probability Distributions: Discrete Probability Distributions: Uniform, Bernoulli, Binomial Distribution and Poisson distribution. Continuous Probability Distributions: Normal and exponential distribution.
Unit-II
Sampling and Testing of Hypothesis: Basic sampling models, sampling distribution of mean and standard deviation, testing of hypothesis, level of significance, confidence intervals for known and unknown means, simple sampling of attributes, tests of significance for large samples, comparison of large samples, central limit theorem, test of significance for two large samples. Student’s t- test, Chi-square test, Goodness of fit, F-distribution.
Unit-III
Solution of System of Linear, Transcendental Equations & Interpolation: Bisection method, Regula-Falsi method Newton Raphson’s method, Gauss elimination method, LU factorization method. Introduction to Interpolation, Lagrange’s interpolation, Newton’s divided difference interpolation, Difference operators and relations.
Unit-IV
Numerical Differentiation & Integration: Numerical differentiation using forward difference, backward difference and central difference formula. Integration by trapezoidal and Simpson’s rules 1/3rd and 3/8th rule.
Numerical Solution of Ordinary Differential Equations: Picard’s method, Taylor series method, Euler’s method, Modified Euler’s method, Runge’s and Runge‐ Kutta method.