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Unit - 1 Basic Probability

1.1 Probability spaces1.2 conditional probability

1.3 independence Discrete random variables

1.4 Independent random variables

1.5 The multinomial distribution

1.6 Poisson approximation to the binomial distribution

1.7 infinite sequences of Bernoulli trials

1.8 sums of independent random variables

1.9 Expectation of Discrete Random Variables

1.10 Moments variance of a sum

1.11 Correlation coefficient

1.12 Chebyshevs Inequality

Unit - 1 Basic Probability

1.1 Probability spaces1.2 conditional probability

1.3 independence Discrete random variables

1.4 Independent random variables

1.5 The multinomial distribution

1.6 Poisson approximation to the binomial distribution

1.7 infinite sequences of Bernoulli trials

1.8 sums of independent random variables

1.9 Expectation of Discrete Random Variables

1.10 Moments variance of a sum

1.11 Correlation coefficient

1.12 Chebyshevs Inequality

Unit - 2 Continuous Probability Distribution

2.1 Continuous random variables and their properties2.2 distribution functions and densities normal exponential and gamma densities

Unit - 2 Continuous Probability Distributions

2.1 Continuous random variables and their properties2.2 distribution functions and densities normal exponential and gamma densities

Unit - 3 Bivariate Distribution

3.1 Bivariate distributions and their properties3.2 distribution of sums and quotients

3.3 conditional densities

3.4 Bayes rule

Unit - 3 Bivariate Distributions

3.1 Bivariate distributions and their properties3.2 distribution of sums and quotients

3.3 conditional densities

3.4 Bayes rule

Unit - 4 Basic Statistics

4.1 Measures of Central tendency Moments skewness and Kurtosis4.2 Probability distributions Binomial Poisson and Normal evaluation of statistical parameters for these three distributions

4.3 Correlation and regression Rank correlation

Unit - 4 Basic statistics

4.1 Measures of Central tendency Moments skewness and Kurtosis4.2 Probability distributions Binomial Poisson and Normal evaluation of statistical parameters for these three distributions

4.3 Correlation and regression Rank correlation

Unit - 5 Applied Statistics

5.1 Curve fitting by the method of least squares fitting of straight lines5.2 second degree parabolas and more general curves

5.3 Test of significance Large sample test for single proportion

5.4 difference of proportions

5.5 single mean difference of means and difference of standard deviations

Unit - 5 Applied statistics

5.1 Curve fitting by the method of least squares fitting of straight lines5.2 second degree parabolas and more general curves

5.3 Test of significance Large sample test for single proportion

5.4 difference of proportions

5.5 single mean difference of means and difference of standard deviations

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