Probability and Statistics syllabus

PCC-253-CYB · Second Year Cyber Security, SPPU 2024 pattern. Every unit, the marks scheme, course outcomes and books, copied from the official syllabus PDF.

PCC-253-CYB2 h/week theoryCCE 40 + End-sem 60

30hours of theory

05.units

02.credits

Unit-wise syllabus

UNIT I

Probability Basics and distributions

6 hours

Conditional and Total Probabilities, Bayes theorem, Random variables, Discrete Probability Distributions- Binomial, Poisson, Geometric distribution, Continuous Probability Distribution: Normal, standard normal, uniform, exponential distribution.

UNIT II

Central limit theorem

6 hours

Central limit theorem, Large-Sample Confidence Intervals for a Population Mean, Confidence Intervals for Proportions, Small-Sample Confidence Intervals for a Population Mean, Confidence Intervals for the Difference Between Two Means, Confidence Intervals for the Difference Between Two Proportions, Small-Sample Confidence Intervals for the Difference Between Two Means, Confidence Intervals with Paired Data.

UNIT III

Sampling Theory and Statistical Estimation

6 hours

Population and Sample, Statistical inference, Sampling with and without replacement, Population parameters, Sample statics, Sampling distributions, Sample mean, Sampling distribution of means, Sample variances, Sampling distribution of variances, Case where population variances is unknown, Unbiased estimates and efficient estimates, point estimate and Interval Estimates

UNIT IV

Test of hypothesis

6 hours

Statistical hypothesis, Null and Alternate hypothesis, test of hypothesis and significance, Type I and Type II errors, Level of Significance, Tests involving the Normal distribution, One-Tailed and Two- Tailed tests, P value. Special tests of significance for large samples and small samples (F, chi-square, z, t-test)

UNIT V

Correlation and regression

6 hours

Introduction of correlation, correlation analysis, coefficient of correlation, probable error, regression, regression analysis, line of regression, standard error of estimate, Rank of correlation. Single and multiple regression.

Marks and credits

Head	Marks	Credit
CCE (continuous comprehensive evaluation)	40	2
End-semester exam	60	2

Prerequisite: Basics of Integration and differentiation, Concepts of set theory.

Course outcomes

CO1Apply probability distributions, Bayes’ theorem, and statistical measures for data analysis and decision-making.
CO2Apply the Central Limit Theorem and construct confidence intervals to estimate and compare population parameters.
CO3Apply statistical inference techniques to estimate population parameters from sample data.
CO4Perform hypothesis testing and statistical analysis for decision-making.
CO5Apply correlation and regression methods to interpret data trends and make predictions.

Books

Text books

Statistics for Engineers and Scientists, Fourth Edition, William Navidi, McGraw-Hill publications
Schaum’s outline of “Probability and Statistics”, Fourth Edition

Reference books

Sheldon M. Ross, “Probability and Statistics for Engineers and Scientists”, Fifth Edition, ELSEVIER Publication
William Feller, An introduction to probability theory and its applications.
Douglas C. Montgomery, George C. Runger, Applied Statistics and Probability for Engineers, Wiley, Year- 2018, ISBN- 1119409535
Johnson Richard A., Miller I., Freund J.E., (2016), “Probability and Statistics for Engineers”, 9th edition, PHI publications
Rao G. S., (2018), “Probability and Statistics for Science and Engineering”, 11th edition, Universities press publication – G Shankar Rao
Douglas C. Montgomery, Elizabeth A. Peck, G. Geoffrey Vining, Introduction to Linear Regression Analysis, Wiley, 2012
Advanced Engineering Mathematics by Erwin Kreyszig (Wiley Eastern Ltd.).(ISBN 978-0-470- 45836-5.)
All of Statistics: A Concise Course in Statistical Inference" by Larry Wasserman (Springer publication). E-Book

FAQ

How many units are in Probability and Statistics?

Probability and Statistics (PCC-253-CYB) has 5 units and 30 hours of theory: Unit I Probability Basics and distributions (6 h); Unit II Central limit theorem (6 h); Unit III Sampling Theory and Statistical Estimation (6 h); Unit IV Test of hypothesis (6 h); Unit V Correlation and regression (6 h).

What is the marks scheme for Probability and Statistics?

The official Cyber Security 2024 pattern syllabus lists continuous comprehensive evaluation (CCE) for 40 marks and the end-semester exam for 60 marks, for 2 credits.

What should I know before Probability and Statistics?

Prerequisite listed in the syllabus: Basics of Integration and differentiation, Concepts of set theory.