Probability and Statistics (Optional Paper)
Classical Theory of Probability, Law of total and compound probability, Conditional probability, Baye’s theorem (simple question based on the theorem).Random variable, discrete and continuous random variables.
Distribution function, probability mass function and probability density function. Bi-variate distributions Conditional and marginal distributions, Conditional expectation & variance. Co-varaiance. Analysis of bivariate data
Mathematical expectation & moment generating functions.Theoretical Discrete Distributions: Binomial and Poisson distributions with mean & variance, Poisson distribution as limiting case of Binomial distribution.
Theoretical Continuous Distribution: Normal distribution with its properties, Simple questions based on area property. Fitting of curves: Principle of curve fitting, fitting of straight line and second degree parabola by least squares method.
Correlation: Definition and types, properties of correlation, methods of studying correlation- Karl Pearson’s coefficient of correlation and Spearman Rank Correlation
Linear Regression - Definition, Fitting of two lines of regression, Regression coefficients with simple properties.
1. Chakravarthy, I.M., Handbook of Applied Statistics , (Willey).
2. Feller, W., Introduction to Probability Theory and its Applications, (Willey - Eastern).
3. Mood, A.M., Graybill, F.,Introduction to the Theory of Statistics , (Mc-Grawhill).
1. Gnedenko, B.: The Theory of Probability (MIR, Moscow).
2. Gupta S.C. , Kapoor V.K., Fundamentals of Statistics Sultan Chand & Sons(2014).
3. Kapoor, Saxena, Mathematical Statistics, S.Chand Publications(1960).
