PROBABILITY AND STATISTICS (Optional Paper)
Classical theory of probability, Laws of total and compound probability, Conditional probability, Baye’s theorem and related problems, 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 and variance, Co-variance, Analysis of bi-variate data.
Mathematical expectation and moment generating functions, Theoretical discrete distributions: Binomial and Poisson distributions with mean and variance, Poisson distribution as limiting case of binomial distribution.
Theoretical continuous distribution: Normal distribution with its properties related problems, 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, Spearman Rank Correlation, Linear Regression: Definition, Fitting of two lines of regression, Regression coefficients with simple properties.
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