MA7155 APPLIED PROBABILITY AND STATISTICS Syllabus
OBJECTIVES:
To introduce the basic concepts of one dimensional and two dimensional Random Variables.
To provide information about Estimation theory, Correlation, Regression and Testing of hypothesis.
To enable the students to use the concepts of multivariate normal distribution and principle components analysis.
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,2 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.
OUTCOME:
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.
OBJECTIVES:
To introduce the basic concepts of one dimensional and two dimensional Random Variables.
To provide information about Estimation theory, Correlation, Regression and Testing of hypothesis.
To enable the students to use the concepts of multivariate normal distribution and principle components analysis.
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,2 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.
OUTCOME:
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.