PROBABILITY AND STATISTICS (1BMATCV301)

PROBABILITY AND STATISTICS

Course Code 1BMATCV301 
Scheme 2025
Type of Course Applied Science Course (ASC) 
Semester III
Teaching Hours/Week (L: T: P) 70 (3:2:0) 
CIE Marks 50
Total Hours of Pedagogy per semester CI (L /T):LI(P):SL&TW: 120 (42:28:0:50)
SEE Marks 50
Credits 4 
Total Marks 100
Examination type (SEE) Theory 
Exam Hours 03

Module-1

DESCRIPTIVE STATISTICS: Role of statistics in engineering; types of data, scales of measurement, collection and presentation of data. Frequency distribution, histograms, bar diagrams, pie charts, and box plots. Measures of central tendency: mean, median, and mode for grouped and ungrouped data. Measures of dispersion: range, variance, standard deviation, and coefficient of variation. Concept of skewness and kurtosis.

(RBT Levels: LI, L2 and L3) Number of Hours: 14

Module-2

PROBABILITY AND RANDOM VARIABLES

Review on sample space, events, axioms of probability, conditional probability, independence of events, total probability theorem, and Bayes theorem.

Random variables, discrete and continuous types, probability mass function, probability density function, cumulative distribution function. Expectation and variance. Joint distributions for two discrete variables.

(RBT Levels: LI, L2 and L3) Number of Hours: 14

Module-3

PROBABILITY DISTRIBUTIONS

Discrete distributions: Binomial, Geometric, and Poisson - definitions, mean, and variance.

Continuous distributions: Uniform, exponential, and normal - definitions, mean, and variance and related problems.

(RBT Levels: LI, L2 and L3) Number of Hours: 14

Module-4

SAMPLING AND ESTIMATION

Sampling concepts: population, sample, parameter, statistic, random sampling, bias, and standard error.

Sampling distributions and central limit theorem. Point estimation and interval estimation. Confidence intervals for mean and proportion.

Hypothesis testing: null and alternative hypotheses, type I and type II errors, one-tailed and two-tailed tests. Basic tests for mean and proportion for large sample; student’s t-distribution, chi-square test for goodness of fit.

(RBT Levels: LI, L2 and L3) Number of Hours: 14

Module-5: 

CORRELATION, REGRESSION

Statistics: Principles of least squares; curve fitting by the method of least squares in the form: 𝑦 = 𝑎 + 𝑏𝑥, 𝑦 = 𝑎 + 𝑏𝑥 + 𝑐𝑥2, 𝑦 = 𝑎𝑥𝑏, and 𝑦 = 𝑎𝑒𝑏𝑥. Correlation, Coefficient of correlation, Lines of regression, Angle between regression lines, rank correlation. Introduction to multiple regression.

(RBT Levels: LI, L2 and L3) Number of Hours: 14

Suggested Learning

Resources Textbooks:

1. S.C. Gupta and V.K. Kapoor, Fundamentals of Mathematical Statistics, S. Chand Publishing.

2. V.K. Rohatgi and A.K. Md. Ehsanes Saleh, An Introduction to Probability and Statistics, Wiley.

3. S. Ross, A First Course in Probability, Pearson India.

4. R.K. Jain and S.R.K. Iyengar, Advanced Engineering Mathematics, Narosa Publishing House.

5. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers.

Reference Books:

1. M.R. Spiegel, J. Schiller, and R.A. Srinivasan, Schaum’s Outline of Probability and Statistics, McGraw Hill.

2. A.M. Mood, F.A. Graybill, and D.C. Boes, Introduction to the Theory of Statistics, McGraw Hill.

3. S. C. Gupta, Statistical Methods, S. Chand Publishing.

4. R. Ramakrishnan, Statistics for Engineers and Scientists, Tata McGraw Hill.