Syllabus

Estimation Theory (6 hours):
Estimators: Unbiasedness, Consistency, Efficiency and Sufficiency, Maximum Likelihood Estimation, Method of moments.

Testing of Hypothesis (6 hours):
Tests based on Normal, t, X2, and F distributions for testing of means, variance, and proportions, Analysis of r x c tables, and Goodness of fit.

Correlation and Regression (8 hours):
Multiple and Partial Correlation, Method of Least Squares, Plane of Regression, Properties of Residuals, Coefficient of Multiple Correlation, Coefficient of Partial Correlation, Multiple Correlation with total and partial correlations, Regression and Partial correlations in terms of lower order coefficients.

Design of Experiments (8 hours):
Analysis of variance, One-way and two-way classifications, completely randomized design, Randomized block design, Latin square design.

Multivariate Analysis (8 hours):
Random vectors and Matrices, Mean vectors, Covariance matrices, Multivariate Normal density and its properties, Principal components: Population principal components, Principal components from standardized variables.

To enable students to estimate the value of the parameters involved in the specific distribution

To give an idea of testing the statistical hypothesis claimed based on a set of data points using suitable test statistics that follow standard sampling distributions.

To establish a relationship that makes it possible to predict one or more variables in terms of others using correlation and regression analysis.

To introduce the various experimental designs and their corresponding analysis of variance, which play a vital role in many real-time scenarios and impart knowledge of handling random vectors representing random variables in multi-dimensional space.

The students will learn to obtain the value of the point estimators using the method of moments and the method of maximum likelihood.

The students will learn to use various test statistics in hypothesis testing for the mean and variances of large and small samples.

The students will be able to determine the regression line using the least square method and calculate the partial and multiple correlation coefficients for the given data points.

The students can test the hypothesis using one-way, two-way, or three-way classifications.

The students can get exposure to the principal component analysis of random vectors and matrices.

J.L. Devore, Probability, and Statistics for Engineering and the Sciences, Thomson and Duxbury, Singapore

S.C. Gupta, and V.K. Kapoor, Fundamentals of Mathematical Statistics, Sultan Chand and Sons

R. A. Johnson, and C. B. Gupta, Miller and Freund's Probability and Statistics for Engineers, Pearson Education

R.A. Johnson, and D.W. Wichern, Applied Multivariate Statistical Analysis, Pearson Education

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