Probability, Statistics and Linear Algebra

UNIT I

• Probability - Probability spaces, conditional probability, independence; 
• Discrete randomvariables, continuous random variables and their properties, 
• Distribution functions and densities, exponential and gamma densities. 
• Independent random variables, the multinomial distribution, 
• Chebyshev's Inequality, Bayes' rule. 

UNIT II

• Basic Statistics- Measures of Central tendency: Moments, skewness 
• Kurtosis - Probability distributions: Binomial, Poisson and Normal 
• Evaluation of statistical parameters for these three distributions, 
• Correlation and regression – Rank correlation. 

UNIT III

• Applied Statistics- Curve fitting by the method of least squares
• Fitting of straight lines, second degree parabolas and more general curves. 
• Test of significance- large sample test for single proportion, 
• Difference of proportions, single mean, difference of means, 
• Difference of standard deviations. 

UNIT IV

• Linear Algebra- Cramer's rule, 
• Singular Value decomposition, 
• Euclidian vector spaces, Projection. 
• Hermitian and Unitary Matrix, 
• Gram -Schmidt orthogonalization, 
• LUdecomposition.