Statistics
Total Marks – 100
1. Basic probability: Axiomatic definition of probability, random variable, distribution function, probability density function, mathematical expectation, conditional probability, jointly distributed random variables, marginal and conditional distribution, conditional expectation, stochastic independence
2. Some special distributions: Binomial, Poisson, negative binomial, hyper geometric, normal distributions with their derivation of their mean and variance. Definition and application of chi square, “T” and “F” distributions
3. Statistical inference: Maximum likelihood estimation of the mean and the variance of a normal population. Confidence interval for mean, difference of means and for variance, testing hypothesis for the equality of two means (paired and unpaired observations), testing of equality of several means (ANOVA) and testing of variance and equality of two variance
4. Correlation and regression: Simple linear regression model, point and interval estimation of parameters. Simple, partial, multiple correlation and testing of these correlations
5. Sampling, simple random, stratified, systematic and cluster sampling, estimates of mean and total and their precision
6. applications of statistics in social, economic and political problems, public health, crimes, law, social innovations, economic development, socio-political inequality