Probability & Statistics

GANPAT UNIVERSITY

FACULTY OF ENGINEERING & TECHNOLOGY

Programme

Bachelor of Technology

Branch/Spec.

Computer  Science & Engineering (CBA/CS/BDA)

Semester

IV

Version

1.0.0.2

Effective from Academic Year

2022-23

Effective for the batch Admitted in

June 2021

Subject  code

2CSE401

Subject Name

Probability & Statistics                

Teaching scheme

Examination scheme (Marks)

(Per week)

Lecture (DT)

Practical (Lab.)

Total

CE

SEE

Total

L

TU

P

TW

Credit

3

0

1

0

4

Theory

40

60

100

Hours

3

0

2

0

5

Practical

30

20

50

Pre-requisites:

Recursion, Principle of Mathematical induction, Graph Plotting

Learning Outcome:

Upon completion of this course, students will be able to:

• Understand all basic fundamentals of Statistics
• Understand proper interpretation of the system based on parameters of probability distribution.
• Apply knowledge of statistics and Probability to form a mathematical model
• Apply concepts of probability and statistics to process the raw data through simulation and/or programming.

Theory syllabus

Unit

Content

Hrs

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 & Demerits 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.

8

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.

7

3

Skewness, Moments and Kurtosis

Introduction, Symmetrical and Asymmetrical Distributions

2

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.

7

5

Random Variables

Discrete Random Variable, Probability Function, Probability Distribution, Continuous Random Variable, Probability Density Function (PDF), Cumulative Density Function (CDF), Properties of CDF, 2D Random Variables, Joint PDF and CDF, Marginal and Conditional Probability Distributions

9

6

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.

Uniform Distribution:

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

8

7

Correlation

Definition of Correlation, Types of Correlation, Karl Person’s Correlation Coefficients, Correlation Coefficients for Bivariate frequency distribution. Definition of Regression, Regression lines, Regression Coefficients.

4

Practical content

• The practicals will be based on implementation of various statistical methods, probabilistic models and probability distributions.
• Tools can be Excel, Matlab, Octave etc. to perform the practical.

Text Books

1

Probability, Statistics and Random Process by T Veerarajan, TMH.

2

Statistical Methods by S. P. Gupta, Sultan Chand Publication

Reference Books

1

Fundamental of Applied Statistic by S.C. Gupta & V.K. Kapoor , Sultan Chand Publication

2

Probability, random variables and stochastic processes by A. Papoulis and S.U. Pillai, TMH

3

Business Statistics by Prof. H.R. Vyas & Others, B.S. Shah Prakashan

Course Outcomes:

COs

Description

CO1

Understand all basic fundamentals of Statistics

CO2

Understand proper interpretation of the system based on parameters of probability distribution.

CO3

Apply knowledge of statistics and Probability to form a mathematical model

CO4

Apply concepts of probability and statistics to process the raw data through simulation and/or programming.

Mapping of CO and PO