Tuesday, November 3, 2015

MA7155 APPLIED PROBABILITY AND STATISTICS

UNIT I ONE DIMENSIONAL RANDOM VARIABLES

Random variables - Probability function – Moments – Moment generating functions and their properties – Binomial, Poisson, Geometric, Uniform, Exponential, Gamma and Normal distributions – Functions of a Random Variable.

UNIT II TWO DIMENSIONAL RANDOM VARIABLES

Joint distributions – Marginal and Conditional distributions – Functions of two dimensional random variables – Regression Curve – Correlation.

UNIT III ESTIMATION THEORY

Unbiased Estimators – Method of Moments – Maximum Likelihood Estimation - Curve fitting by Principle of least squares – Regression Lines.

UNIT IV TESTING OF HYPOTHESES

Sampling distributions - Type I and Type II errors - Tests based on Normal, t, Chi-Square and F distributions for testing of mean, variance and proportions – Tests for Independence of attributes and Goodness of fit.

UNIT V MULTIVARIATE ANALYSIS

Random Vectors and Matrices - Mean vectors and Covariance matrices - Multivariate Normal density and its properties - Principal components Population principal components - Principal components from standardized variables.

REFERENCES:

1 Jay L. Devore, “Probability and Statistics For Engineering and the Sciences”,Thomson and Duxbury, 2002.

2.Richard Johnson. ”Miller & Freund’s Probability and Statistics for Engineer”, Prentice – Hall , Seventh Edition, 2007.

3.Richard A. Johnson and Dean W. Wichern, “Applied Multivariate Statistical Analysis”, Pearson Education, Asia, Fifth Edition, 2002.

4.Gupta S.C. and Kapoor V.K.”Fundamentals of Mathematical Statistics”, Sultan an Sons, 2001. 5.Dallas E Johnson , “Applied Multivariate Methods for Data Analysis”, Thomson an Duxbury press,1998.