MA4151 Applied Probability and Statistics for Computer Science Engineers Syllabus:
MA4151 Applied Probability and Statistics for Computer Science Engineers Syllabus – Anna University PG Syllabus Regulation 2021
COURSE OBJECTIVES:
To encourage students to develop a working knowledge of the central ideas of Linear Algebra.
To enable students to understand the concepts of Probability and Random Variables.
To understand the basic probability concepts with respect to two dimensional random variables along with the relationship between the random variables and the significance of the central limit theorem.
To apply the small / large sample tests through Tests of hypothesis.
To enable the students to use the concepts of multivariate normal distribution and principal components analysis.
UNIT I LINEAR ALGEBRA
Vector spaces – norms – Inner Products – Eigenvalues using QR transformations – QR factorization – generalized eigenvectors – Canonical forms – singular value decomposition and applications – pseudo inverse – least square approximations.
UNIT II PROBABILITY AND RANDOM VARIABLES
Probability – Axioms of probability – Conditional probability – Baye’s theorem – Random variables – Probability function – Moments – Moment generating functions and their properties – Binomial, Poisson , Geometric, Uniform, Exponential, Gamma and Normal distributions – Function of a random variable.
UNIT III TWO DIMENSIONAL RANDOM VARIABLES
Joint distributions – Marginal and conditional distributions – Functions of two-dimensional random variables – Regression curve – Correlation.
UNIT IV TESTING OF HYPOTHESIS
Sampling distributions – Type I and Type II errors – Small and Large samples – 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.
TOTAL : 60 PERIODS
COURSE OUTCOMES:
At the end of the course, students will be able to
CO1:apply the concepts of Linear Algebra to solve practical problems.
CO2:use the ideas of probability and random variables in solving engineering problems.
CO3:be familiar with some of the commonly encountered two dimensional random variables and be equipped for a possible extension to multivariate analysis.
CO4:use statistical tests in testing hypotheses on data.
CO5:develop critical thinking based on empirical evidence and the scientific approach to knowledge development.
REFERENCES:
1. Dallas E Johnson, “Applied multivariate methods for data Analysis”, Thomson and Duxbury press, Singapore, 1998.
2. Richard A. Johnson and Dean W. Wichern, “Applied multivariate statistical Analysis”, Pearson Education, Fifth Edition, 6th Edition, New Delhi, 2013.
3. Bronson, R.,”Matrix Operation” Schaum’s outline series, Tata McGraw Hill, New York, 2011.
4. Oliver C. Ibe, “Fundamentals of Applied probability and Random Processes”, Academic Press, Boston, 2014.
5. Johnson R. A. and Gupta C.B., “Miller and Freund’s Probability and Statistics for Engineers”, Pearson India Education, Asia, 9th Edition, New Delhi, 2017.