MA7155 Syllabus - Applied Probability and statistics

MA7155                     APPLIED PROBABILITY AND STATISTICS                         L T P C

 3 1 0 4

OBJECTIVES:

 1.To introduce the basic concepts of one dimensional and two dimensional Random

Variables.

 2.To provide information about Estimation theory, Correlation, Regression and Testing of

hypothesis.

 3.To enable the students to use the concepts of multivariate normal distribution and

principle components analysis.

UNIT I ONE DIMENSIONAL RANDOM VARIABLES                                                                     9+3
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                                                       9+3
Joint distributions – Marginal and Conditional distributions – Functions of two dimensional

random variables – Regression Curve – Correlation.

UNIT III ESTIMATION THEORY                                                                                         9+3
 Unbiased Estimators – Method of Moments – Maximum Likelihood Estimation - Curve fitting

by Principle of least squares – Regression Lines.

UNIT IV TESTING OF HYPOTHESES                                                                                    9+3
Sampling distributions - Type I and Type II errors - Tests based on Normal, t,2 and F

distributions for testing of mean, variance and proportions – Tests for Independence of

attributes and Goodness of fit.

UNIT V MULTIVARIATE ANALYSIS                                                                                                9+3
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.

TOTAL                                                                                                            45+15=60 PERIODS

OUTCOME:

1. The student will able to acquire the basic concepts of Probability and Statistical

techniques for solving mathematical problems which will be useful in solving Engineering

problems

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.