MA3302 Transforms and Statistics Syllabus:

MA3302 Transforms and Statistics Syllabus – Anna University Regulation 2021

COURSE OBJECTIVES

 To acquaint the student with Fourier Series techniques used in wide variety of situations in which the functions used are not periodic and to solve boundary value problems.
 To understand the Fourier transform techniques to solve boundary value problems.
 To introduce the concept of Probability and random variables in Statistics which is central to many geometric applications.
 To introduce the basic concepts of two dimensional random variables.
 To acquaint the knowledge of testing of hypothesis for small and large samples which plays an important role in real life problems.

UNIT I FOURIER SERIES

Dirichlet’s conditions – General Fourier series – Odd and even functions – Half-range Sine and cosine series – Root mean square value – Parseval’s identity – Harmonic Analysis.

UNIT II FOURIER TRANSFORM

Fourier integral theorem – Fourier transform pair – Sine and cosine transforms – Properties – Transform of elementary functions – Convolution theorem – Parseval’s identity.

UNIT III RANDOM VARIABLES

Discrete and continuous random variables – Moments – Moment generating functions – Binomial, Poisson, Geometric, Uniform, Exponential and Normal distributions – Functions of a random variable.

UNIT IV TWO-DIMENSIONAL RANDOM VARIABLES

Joint distributions – Marginal and conditional distributions – Covariance – Correlation and Linear regression – Transformation of random variables – Central limit theorem (for independent and identically distributed random variables).

UNIT V ESTIMATION THEORY

Unbiased estimators – Efficiency – Consistency – Sufficiency – Robustness – Method of moments – Method of maximum Likelihood – Interval estimation of Means – Differences between means, variations and ratio of two variances.

TOTAL: 60 PERIODS
COURSE OUTCOMES:

On completion of the course, the student is expected to
CO1 Apply Fourier series techniques used in wide variety of situations in which the functions used are not periodic and to solve boundary value problems.
CO2 Apply the Fourier transform techniques to solve boundary value problems.
CO3 To understand and apply the concept of Probability and random variables in Statistics which is central to many geometric applications.
CO4 To apply the basic concepts of two dimensional random variables.
CO5 To understand the knowledge of applying the concept of estimation theory which plays an important role in real life problems.

TEXTBOOKS:

1. Grewal. B.S., “Higher Engineering Mathematics”, Khanna Publishers, New Delhi, 44th Edition, 2018.
2. John E. Freund’s “Mathematical Statistics with Applications”, 8th Edition, Pearson Education, New Delhi, 2017.
3. Milton. J. S. and Arnold. J.C., “Introduction to Probability and Statistics”, Tata McGraw Hill, New Delhi, 4th Edition, 3rd Reprint, 2008.

REFERENCES:

1. James. G., “Advanced Modern Engineering Mathematics “, 4th Edition, Pearson Education, New Delhi, 2016.
2. Kreyszig. E, “Advanced Engineering Mathematics”, John Wiley & Sons, 10th Edition, New Delhi, 2014.
3. Devore. J.L., “Probability and Statistics for Engineering and the Sciences”, Thomson Brooks/Cole, International Student Edition, New Delhi, 8th Edition, 2012.
4. Ross. S.M., “Introduction to Probability and Statistics for Engineers and Scientists”, Elsevier, New Delhi, 5th Edition, 2014.
5. Spiegel. M.R., Schiller. J. and Srinivasan. R.A., “Schaum’s Outline of Theory and Problems of Probability and Statistics”, Tata McGraw Hill, New Delhi, 2004.