Unit 1

Introduction to Statistics: Statistical Methods: Definition and scope of Statistics, concepts of statistical population and sample. Data: quantitative and qualitative, attributes, variables, scales of measurement
-nominal, ordinal, interval and ratio. Presentation: tabular and graphical, including histogram and ogives, consistency and independence of data with special reference to attributes.

Unit 2

Measures of Central Tendency: mathematical and positional-Measures of Dispersion: range, quartile deviation, mean deviation, standard deviation, coefficient of variation, Moments, absolute moments, factorial moments, skewness and kurtosis, Sheppard’s corrections.

Unit 3

Bivariate data: Definition, scatter diagram, simple, partial and multiple correlation (Three variables only), rank correlation. Simple linear regression, principle of least squares and Fitting of polynomials and exponential curves.

Unit 4

Elements of Probability: Introduction, random experiments, sample space, events and algebra of events. Axioms of Probability, Sample Spaces Having Equally Likely Outcomes, Conditional Probability, Bayes’ Formula, Independent Events.

Unit 5

Univariate Random Variables, Types of Random Variables, Expectation, higher moments and moment generating function of random variables, Chebychev’s Inequality.
Special Random Variables and Their Distributions: Bernoulli, Binomial, Poisson and Geometric Random Variables and their distributions, moments and special properties, Uniform, Exponential gamma and Normal Random Variables and their distributions, moments and special properties.

Course Outcomes

On successful completion of the course, students shall be able to

CO1: apply the basic statistical concepts and graphical representations of the data for examples CO2: apply different measures of central tendency and interpret the trends in behaviour of statistical data.
CO3: apply the basic knowledge on fundamental probability concepts, probability of an event, additive rules and conditional probability and Bayes’ theorem for solving basic problems.
CO4: apply the concepts of random variables, probability distributions to calculate moments of distributions
CO5: apply the concepts of standard discrete and continuous distributions in one dimensions to solve simple problems.

Textbook:

1. D.C. Montgomery and G.C. Runger, Applied Statistics and Probability for Engineers, John Wiley and Sons.

References:

1. Ross S.M., Introduction to Probability and Statistics for Engineers and Scientists, 3rd edition, Elsevier Academic Press.
2. J. Ravichandran, Probability and Statistics for Engineers, Wiley.
3. Hogg, R.V., Tanis, E.A. and Rao J. M., Probability and Statistical Inference, Seventh Ed, Pearson Education, New Delhi.

K.L. Chung, Elementary Probability Theory: With Stochastic Processes and an Introduction to Mathematical Finance, Springer.