Course Name :Probability and Statistics
Still no participant
Still no reviews
Course Name :Probability and Statistics
Code(Credit) : CUTM1524(3-1-2)
• To translate real-world problems into probability models.
• To motivate students in an intrinsic interest in statistical thinking.
• T o apply probability and statistics in engineering and science like disease modeling, climate prediction and computer networks etc.
Upon successful completion of this course, students will be able to:
COs | Course Outcomes | Mapping with COs with POs
(High-H, Low-L, Medium-M) |
CO1 | Define and illustrate the concepts of sample space, events and compute the probability and conditional probability of events. | PO1(3), PO9(2) |
CO2 | Define, illustrate and apply the concepts of discrete and continuous random variables, the discrete and continuous
probability distributions. |
PO4(3), PO2(2) |
CO4 | Define, illustrate and apply the concept of the expectation to the mean, variance and covariance of random variables. | PO3(2) |
CO5 | Compute probabilities based on practical situations using the Binomial, Poisson and Normal distributions. | PO5(2), PO9(2) |
Module I: (4 hrs+2 hrs+4hrs)
Probability: Axiomatic definitions of probability, Sample Space, Probability axioms, Independent events, Mutually Exclusive Event, Equally Likely Events
Practice-1(2 hrs)
Bayes Theorem using MATLAB
Project-1 (2hrs)
Application of conditional probability analysis to the clinical diagnosis
Project-2(2hrs)
A Report on Bayes’ Theorem and its Application in Different Fields
Module II:(4 hrs+2 hrs+4hrs)
Discrete random variables, Continuous random variables, Expectation of random variables,Variance and Standard Deviation
Practice-2(2hrs)
Probability Density Function using MATLAB
Project-3(2hrs)
A Report on Random Variables with Examples
Project-4 (2hrs)
A Report on Moment Generating Function of Distributions
Module III:(6 hrs+4 hrs+4hrs)
Binomial distribution, Poisson distribution, Poisson Distribution as the limiting case of Binomial Distribution
Practice-3(2 hrs)
Binomial distribution using MATLAB
Practice-4(2 hrs)
Poisson distribution - algorithm in Matlab
Project-5(2hrs)
Comparative study between Binomial distribution and Poisson distribution
Project-6(2hrs)
Report on Poisson distribution with their Business Applications in analyzing
data sets
Module IV:(4 hrs+2hrs+8hrs)
Uniform distribution, Normal distributions, Normal approximation to the Binomial distributions
Practice-5(2hrs)
Gaussian distribution – how to plot it in Matlab
Project -7(2hrs)
Flip class
A Report on Gamma, Exponential, Beta Distributions
Project-8(2hrs)
A Report on Central Limit Theorem (CLT) and its Applications in election polls
Project-9(2hrs)
Flip class
A Report on Negative binomial Distribution
Project-10(2hrs)
Flip class
A Report on Geometric distributions
Module V:(4 hrs+0 hr+0 hr)
Distribution of two random variables, Expectation of function of two random variables
Module VI:(4 hrs)
Conditional distributions and expectations.
Module VII:(4 hrs+2 hrs+4hrs)
Correlation coefficient, Co-variance independent random variables, linear regression of two variables
Practice-6(2hrs)
Covariance & Correlation Coefficient calculation in MATLAB
Project-11 (2hrs)
Flip Class
A Report on Markov’s inequality
Project -12(2hrs)
Flip Class
A Report on Chebyshev’s inequality
Total Hrs=T(30hrs+P(12hrs)+Pj(24hrs))
Text Books:
1. Irwin Miller and Marylees Miller, John E. Freund, Mathematical Statistics with Applications, 7th Ed., Pearson Education, Asia, 2006.
2. Sheldon Ross, Introduction to Probability Models, 9th Ed., Academic Press, Indian Reprint, 2007.
Reference Books:
1. Statistical Methods By S.P. Gupta (31st Edition) ; Publisher: Sultan Chand & Sons
2. Mathematical Statistics By S.C. Gupta & V.K. Kapur(10th Edition); Publisher: Sultan Chand & Sons.
Course outline Prepared by: Dr.Banitamani Mallik
Date:08-06-2020
Source of reference: udemy,coursera, Harvard University
Note: 1 credit theory=10 hrs lecture, 1 credit practice/project=12.5 hrs lab/workshop/field work in a semester
Axiomatic definitions of probability, Sample Space
Web Link
https://www.youtube.com/watch?v=ZA4JkHKZM50
Probability axioms, Independent events
Web Link
https://www.youtube.com/watch?v=LS-_ihDKr2M
Mutually Exclusive Event, Equally Likely Events
Web Link
https://www.youtube.com/watch?v=7ZK6HuF61pY
Independent and Dependent Events
Web Link
https://www.youtube.com/watch?v=LS-_ihDKr2M.
Bayes Theorem
Web Link
https://www.youtube.com/watch?v=XQoLVl31ZfQ.
Practice-1
Bayes Theorem using MATLAB
https://www.youtube.com/watch?v=dhsK-mRzxFw
Project-1
Conditional probability
Web Link
https://www.youtube.com/watch?v=zuQUpShD3ZQ.
Project-1
Application of conditional probability analysis to the clinical diagnosis
Project-2
A Report on Bayes’ Theorem and its Application in Different Fields
Web Link
https://www.youtube.com/watch?v=HZGCoVF3YvM
A Report on Bayes’ Theorem and its Application in Different Fields
Web Link
https://www.youtube.com/watch?v=U_85TaXbeIo.
Discrete random variables
Web Link
https://www.youtube.com/watch?v=lHCpYeFvTs0
Continuous random variables
Web Link
https://www.youtube.com/watch?v=UVQs9zikfe0
Expectation of random variables
Web Link
https://www.youtube.com/watch?v=8i9WUZhpxPE
Variance and Standard Deviation
Web Link
https://www.youtube.com/watch?v=MRqtXL2WX2M
Practice-2
Probability Density Function using MATLAB
Web Link
https://www.youtube.com/watch?v=8N2fZEKqZhg
Practice-2
Probability Density Function using MATLAB
Web Link
https://www.youtube.com/watch?v=8N2fZEKqZhg.
Project-3
A Report on Random Variables with Examples
Web Link
https://www.youtube.com/watch?v=ynJFdCrYvdU.
Project-3
A Report on Random Variables with Examples
Moment Generating Function of Distributions
Web Link
https://www.youtube.com/watch?v=MENmUBNEDv8.
Project-4
A Report on Moment Generating Function of Distributions
Web Link
https://www.youtube.com/watch?v=l2sx5_e7mIo.
Binomial distribution
Web Link
https://www.youtube.com/watch?v=8idr1WZ1A7Q
Binomial distribution
Binomial distribution
Poisson distribution
Web Link
https://www.youtube.com/watch?v=O-YhNpy7z3I
Poisson distribution
Poisson Distribution as the limiting case of Binomial
Distribution
Web Link
https://www.youtube.com/watch?v=cmWFNOS0v9w.
Practice-3
Binomial distribution using MATLAB
Web Link
http://www.matrixlab-examples.com/binomial-distribution.html
Practice-3
Binomial distribution using MATLAB
Web Link
https://www.youtube.com/watch?v=Vub3nSjldiU.
Practice-4
Poisson distribution - algorithm in Matlab
Web Link
http://www.matrixlab-examples.com/poisson-distribution.html
Practice-4
Poisson distribution - algorithm in Matlab
Web Link
https://www.youtube.com/watch?v=yqjME6zcr5I.
Project-5
Comparative study between Binomial distribution and Poisson distribution
Web Link
https://www.youtube.com/watch?v=eexQyHj6hEA.
Project-5
Comparative study between Binomial distribution and Poisson distribution
Web Link
https://www.youtube.com/watch?v=i1DydN7J2z4.
Project-6
Report on Binomial and Poisson distribution with their Business Applications in analyzing data sets
Web Link
https://www.youtube.com/watch?v=BbLfV0wOeyc.
Project-6
Report on Binomial and Poisson distribution with their Business Applications in analyzing data sets
Web Link
https://www.youtube.com/watch?v=Fk02TW6reiA.
Uniform distribution
Web Link
https://www.youtube.com/watch?v=wnh7Zj2NYNw
Normal distributions
Web Link
https://www.youtube.com/watch?v=mtbJbDwqWLE&pbjreload=101
Normal distributions
Normal approximation to the Binomial distributions
Web Link
https://www.youtube.com/watch?v=A2sd09qCvcg
Practice-5
Gaussian distribution – how to plot it in Matlab
Web Link
http://www.matrixlab-examples.com/gaussian-distribution.html
Gaussian distribution
Web Link
https://www.youtube.com/watch?v=mtH1fmUVkfE.
Project-7
Flip class
A Report on Gamma Distributions
Web Link
https://www.youtube.com/watch?v=gIsoceE4vhg.
Project-7
A Report on Exponential, Beta Distributions
Web Link
https://www.youtube.com/watch?v=onBoUN5qlXg.
Project-8
A Report on Central Limit Theorem (CLT) and its Applications in election polls
Web Link
https://www.youtube.com/watch?v=b5xQmk9veZ4.
A Report on Central Limit Theorem (CLT) and its Applications in election polls
Web Link
https://www.youtube.com/watch?v=N7wW1dlmMaE.
Project-9
Flip class
A Report on Negative binomial Distribution
Web Link
https://www.youtube.com/watch?v=UUzRsQ-8vC8.
Project-9
Flip class
A Report on Negative binomial Distribution
Web Link
https://www.youtube.com/watch?v=IBBESd4rU1I.
Project-10
Flip class
A Report on Geometric distributions
Web Link
https://www.youtube.com/watch?v=zq9Oz82iHf0.
Project-10
Flip class
A Report on Geometric distributions
Web Link
https://www.youtube.com/watch?v=LRchV_OrMzw.
Joint Probability Distribution of two random variables
Web Link
https://www.youtube.com/watch?v=_lmwI1sGihA
Joint Probability Distribution of two random variables
Web Link
https://www.youtube.com/watch?v=759IvlC3yKY.
Expectation of function of two random variables
Web Link
https://www.youtube.com/watch?v=6GfR-WHcbLI
Expectation of function of two random variables
Web Link
https://www.youtube.com/watch?v=6GfR-WHcbLI.
Conditional distributions and expectations
Web Link
https://www.youtube.com/watch?v=XzZYnq10lMU
Conditional distributions and expectations
Web Link
https://www.youtube.com/watch?v=strrrdJivco.
Conditional distributions and expectations
Web Link
https://www.youtube.com/watch?v=XzZYnq10lMU
Conditional distributions and expectations
Web Link
https://www.youtube.com/watch?v=uYbThumrD14.
Correlation coefficient
Web Link
https://www.youtube.com/watch?v=lVOzlHx_15s
PPT16(Uses of regression and correlation analysis in bussines )
Co-variance independent random variables
Web Link
https://www.youtube.com/watch?v=CY2R4sz_ww8
Linear Regression of two variables
Web Link
https://www.youtube.com/watch?v=zPG4NjIkCjc
Linear Regression of two variables
Web Link
https://www.youtube.com/watch?v=K_EH2abOp00.
Practice-6
Covariance & Correlation Coefficient calculation in MATLAB
Web Link
https://www.youtube.com/watch?v=18U1G_35boU
Practice-6
Covariance & Correlation Coefficient calculation in MATLAB
Web Link
https://www.youtube.com/watch?v=u1p4Nz6wZHM.
Project-11
Flip Class
A Report on Markov’s inequality
Web Link
https://www.youtube.com/watch?v=5xc48m2k4G8.
Project-11
Flip Class
A Report on Markov’s inequality
Web Link
https://www.youtube.com/watch?v=cd7ntlIRKuU.
Project-12
Flip Class
A Report on Chebyshev’s inequality
Web Link
https://www.youtube.com/watch?v=d5pnfFvggYk.
Project-12
Flip Class
A Report on Chebyshev’s inequality
Web Link
https://www.youtube.com/watch?v=CsyoZhiWibs.
Professor ,School of Applied Sciences, Centurion University of Technology and Management, Paralakhemundi, Odisha, India. She has over 26 years of teaching and 8 years of research experiences. She has published 35 research articles in National and International refereed journals and has authored 01 book and 02 book chapters. She has produced 01 PhD scholar and […]