  # Probability & Statistics : 2CSE401

Learning Outcomes:
Upon completion of this course, students will be able to:
• Understand all basic fundamentals of Statistics and its application on collected information.
• Prepare him/her self for making a proper interpretation of system based on parameters of distribution.
• Apply knowledge of statistics and Probability to form a mathematical model to ensure conclusive hypothesis for problem.
Syllabus:
Unit NoTopics
1

Measures Of Central Tendency:

Introduction, Arithmetic Mean, Simple and weighted for raw data, Discrete frequency distribution, Continuous frequency distribution, Properties of A.M., Merits & De merits of A.M., Median for raw data, Discrete frequency distribution, Continuous frequency distribution, Merits and demerits of Median, Mode for raw data, Merits & demerits of mode.

2

Measures Of Dispersion:

Introduction, Range, coefficient of range, Quartiles, Quartiles deviations, coefficient of quartile deviations, Mean deviation and coefficient of mean deviation, S.D and variance for all types of frequency distribution, Coefficient of Dispersion, Coefficient of variation.

3

Correlation

Definition of Correlation, Types of Correlation, Scatter Diagram Method, Karl Person’s Correlation Coefficients, Correlation Coefficients for Bivariate frequency distribution, Probable error for Correlation Coefficients, Rank Correlation Co-efficient.Definition of Regression, Regression lines, Regression Coefficients

4

Probability Theory:

Introduction, Random Experiment, Sample Space, Events, Complementary Events, Union and Intersection of Two Events, Difference Events, Exhaustive Events, Mutually Exclusive Events, Equally Likely Events, Independent Events, Mathematical & Statistical definition of Probability, Axiomatic definition of probability, Addition Theorem, Multiplication Theorem, Theorems of Probability, Conditional Probability, Inverse Probability.

5

Probability Distributions:

Binomial Distribution:

Introduction, Probability mass function of Binomial distribution, Mean and Variance of Binomial distribution, Properties of Binomial Distribution, Uses of Binomial Distribution.

Poisson Distribution:

Introduction, Probability mass function of Poisson distribution, Mean and Variance of Poisson distribution, Properties of Poisson Distribution, Applications of Poisson Distribution.

Normal Distribution:

Introduction, Probability density function of Normal distribution, Properties of Normal distribution, Importance of Normal Distribution.

6

Hypothesis testing:

Types of Error, Power of a test, Goodness of a fit, Student t and Chi square; Sufficient Statistic and MLEs; Limit theorems and convergence of random variables; Elementary concepts related to stochastic processes; Forecasting and Modelling applications.

7

Random (Stochastic) processes (RP)

Introduction and Definition, continuous and discrete time process, moments of RP, autocorrelation, independence and uncorrelated process, Independent and Identically Distributed Process, its moments: mean, variance, covariance,Wiener process, strict sense stationary (SSS), Wide-sense stationary process (WSS) their mean, variance, autocorrelation function, continuity (mean square) of RP, Time average of RP, mean and variance of time averages, Ergodicity principle, white noise process, band limitation in white noise, Linear systems and signal estimation in presence of noise

Text Books:
Name :
Probability, Statistics and Random Process
Author:
T Veerarajan
Publication:
TMH
Edition:
3rd
Name :
Probability, random variables and stochastic processes
Author:
by A. Papoulis
S.U. Pillai
Publication:
TMH
Reference Books:
Name:
Fundamental of Applied Statistic
Author:
S.C. Gupta
V.K. Kapoor
Publication:
Sultan Chand
Name:
Statistical Methods
Author:
S. P. Gupta
Publication:
Sultan Chand
Name:
Author:
H.R. Vyas & other
Publication:
B.S. Shah
Syllabus PDF:
AttachmentSize PNS.pdf215.09 KB
branch:
CBA
BDA
MA
Cyber Security
Course:
2018
Stream:
B.Tech