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SYllabuS
UNIT I LINEAR ALGEBRA
norms Inner Products
Vector spaces factorization Eigenvalues using QR transformations generalized eigenvectors Canonical forms and applications pseudo inverse least square approximations. singular value decomposition
UNIT II PROBABILITY AND RANDOM VARIABLES
Probability variables properties distributions Axioms of probability Conditional probability - Baye's theorem Random Probability function Moments Moment generating functions and their Binomial, Poisson, Geometric, Uniform, Exponential, Gamma and Normal Function of a random variable.
UNIT III TWO DIMENSIONAL RANDOM VARIABLES
Joint distributions random variables Marginal and conditional distributions Regression curve Correlation. Functions of two dimensional
UNIT IV TESTING OF HYPOTHESIS
Sampling distributions Type I and Type II errors
Small and Large samples Tests based on Normal, t, Chi square and F distributions for testing of mean, variance and proportions Tests for independence of attributes and goodness of fit.
UNIT V MULTIVARIATE ANALYSIS POUCH KNOWLEDGE
Random vectors and matrices Mean vectors and covariance matrices Multivariate normal density and its properties Principal components Principal components from standardized variables. Population principal components