Various Statistical Measures-
Basic probability, sample space, events, axioms of probability conditional probability, independent events. Random variables, continuous/Discrete random variables, exception, valance, convenience, conditional distributions, moment generating functions.
Multiple regressions.
Distributions, Bernoulli, Binomial, Poisson, Uniform, Normal, Exponential, Chisquare T and F.
Sample statistics,
empirical distributions, and goodness of fit, sampling from normal populations.
Parameter estimation, moment method, maximum likelihood, interval estimated. Hypothesis Testing, Significance Intervals.
Numerical Methods Basic: Summary of basic concepts from Linear algebra and numerical analysis, Matrices, Operation counts, Matrix Norms, Type of Errors in Numerical computation.
Matrix Factorization And Linear System :
Cholesky Factorization, QR factorization by House holder matrices Lufactorization and Gaussian elimination, partial pivoting, error Analysis (statement of result) soling triangular system by substitution, solving full systems by factorization. Lu-factorization for banded and sparse matrices, storage schemes, Iterative Methods, Jacobi, Gauss – Seidal and SOR Iterations, Conjugate gradient method, preconditioning.
Numerical Integration Gaussian Quadrature, Romberg Integration, Adaptive Quadrature.
Introduction to: Spss / Sas software / Matlab Statistical Tool Box,Use Of Mathematical Software