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** MA7155 APPLIED PROBABILITY AND STATISTICS SYLLABUS**

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**ME SOFTWARE ENGINEERING****SEMESTER 1**

**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.

-> 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 - Testsbased 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.

**TOTAL 45+15:60 PERIODS**

**OUTCOMES:**

-> 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 and Sons, 2001.

5. Dallas E Johnson, “Applied Multivariate Methods for Data Analysis”, Thomson and Duxbury press, 1998.

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