B V Rao

CMI, Chennai

Real random variables (discrete and continuous), cumulative distribution function, probability mass/density functions, mathematical expectation, moments, moment generating function, characteristic function. Discrete distributions : uniform, binomial, Poisson, geometric, negative binomial, Continuous distributions : uniform, normal, exponential.

Mousumi Bose

ISI, Kolkata

Sampling Distributions : Statictic, Sample moments. Sample variance, Sampling from the normal distributions, Chi-square, t and F-distributions

Estimation of parameters : Point estimation. Interval Estimation- Confidence Intervals for mean and variance of Normal Population. Mean-squared error. Properties of good estimators - unbiasedness, consistency, sufficiency, Minimum-Variance Unbiased Estimator (MVUE).

Method of Maximum likelihood : likelihood function, ML estimators for discrete and continuous models.

Alok Goswami

Indian Association for the Cultivation of Science, Kolkata

Probability II: Joint cumulative distribution function and its properties, joint probability density functions, marginal and conditional distributions, expectation of function of two random variables, moments, covariance, correlation coefficient, independent random variables, joint moment generating function (jmgf) and calculation of covariance from jmgf, characteristic function. Conditional expectations, linear regression for two variables, regression curves. Bivariate normal distribution.

Markov and Chebyshev’s inequality, Convergence in Probability, statement and interpretation of weak law of large numbers and strong law of large numbers. Central limit theorem for independent and identically distributed random variables with finite variance.

Arnab Chakraborty

ISI, Kolkata

Statistics II: Statistical hypothesis : Simple and composite hypotheses, null hypotheses, alternative hypotheses, one- sided and two-sided hypotheses. The critical region and test statistic, type I error and type II error, level of significance. Power function of a test, most powerful test. The p-value (observed level of significance), Calculating p-values.

Simple hypothesis versus simple alternative : Neyman-Pearson lemma (Statement only). Bivariate frequency Distribution : Bivariate data, Scatter diagram, Correlation, Linear Regression, principle of least squares and fitting of polynomials and exponential curves.

Lecture
1 & 2

9.00
to
11.00

Tutorial

11.30
to
12.30

Lecture
3 & 4

2.30
to
4.30

Tea

4.35
to
4.55

Tutorial

5.00
to
6.00

1

2