ABOUT THE COURSE: "Probability Theory for Data Science" is a specialized course designed to equip students with the essential knowledge and skills needed to analyze uncertain phenomena and make data-driven decisions in various domains. It provides a comprehensive understanding of the principles of probability and their applications in the context of data science. This course is essential for anyone aspiring to work in data-driven fields such as machine learning, artificial intelligence, statistics, and predictive analytics. The course typically begins with an introduction to basic concepts in probability theory, including sample spaces, events, and different approaches to defining probability. Emphasis is placed on developing a solid grasp of fundamental probability rules, such as the addition and multiplication rules, as well as understanding conditional probability, independence, and Bayes theorem. As the course progresses, students delve deeper into more advanced topics, such as random variables, probability distributions, and expectation. They explore common probability distributions, including binomial, Poisson, uniform, exponential, and normal distributions, and they learn how to calculate probabilities and expected values associated with these distributions. Additionally, students gain insight into concepts like moments, variance, and covariance, which are crucial for understanding data variability in real-world scenarios. Following this, students delve into the study of multiple random variables, exploring concepts such as the transformation of random variables, moment-generating functions, and key theorems pertaining to the convergence of random variables. "Probability Theory for Data Science" equips students with a strong theoretical foundation in probability and the analytical skills necessary to tackle complex data-driven problems. By mastering the principles of probability theory and its applications in data science, students are better prepared to excel in diverse roles within the rapidly growing field of data analytics and machine learning.
INTENDED AUDIENCE: Graduate students and researchers from Academics and Industry who are interested in Data Science.
PREREQUISITES: 10+2 Mathematics
Summary
Course Status :
Ongoing
Course Type :
Core
Duration :
12 weeks
Category :
Mathematics
Credit Points :
3
Level :
Undergraduate
Start Date :
22 Jul 2024
End Date :
11 Oct 2024
Enrollment Ends :
05 Aug 2024
Exam Registration Ends :
16 Aug 2024
Exam Date :
27 Oct 2024 IST
Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.
Page Visits
Course layout
Week 1:
Phenomena
Definitions: sample space, events
Set operations
Definitions of probability: classical approach, frequency approach, axiomatic
approach
Important theorems
Examples
Conditional probability
Examples
Week 2:
Independence
Mutually exclusive vs. independence
Bayes’ theorem
Examples
Random variable
Events defined by random variables
Examples
Cumulative distribution function
Week 3:
Properties of the cumulative distribution function
Examples
Discrete random variable
Probability mass function
Continuous random variable
Probability density function
Mean
Examples
Week 4:
Moments
Variance
Examples
Bernoulli distribution
Binomial distribution
Poisson distribution
Week 5:
Poisson distribution examples
Uniform distribution
Exponential distribution
Memoryless property
Gamma distribution
Week 6:
Gamma distribution examples
Normal distribution
Examples
Conditional distribution
Conditional probability mass function
Conditional probability density function
Examples
Bivariate random variables
Examples
Joint distribution function
Week 7:
Properties of the joint distribution function
Independence
Marginal distribution function
Examples
Joint probability mass function
Examples
Joint probability density function
Examples
Week 8:
Conditional probability mass functions
Examples
Conditional probability density function
Examples
Moments
Covariance and correlation coefficient
Examples
Week 9:
Conditional mean
Examples
Conditional variance
Examples
Multivariate random variable
Multivariate cumulative distribution function
Multivariate probability mass function
Marginals
Week 10:
Multivariate probability density function
Marginals
Independence
Moments
Examples
Multinomial distribution
Applications
Multivariate normal distribution
Applications
Week 11:
Transformation of random variables: theorems, examples
Transformation of multivariate random variables
Examples
Week 12:
Moment generating function: theorems, examples
Characteristic function
Chebychev’s inequality
Examples
Notion of convergence
The weak law of large numbers
The strong law of large numbers
The central limit theorem
Examples
Books and references
Chung K L, Elementary Probability Theory with Stochastic Process, Springer Verlag (1974)
Drake A, Fundamentals of Applied Probability Theory, McGraw-Hill (1967)
Kreyszig E, Advanced Engineering Mathematics, John Wiley & Sons (2010)
Ross S, A First course in Probability, Prentice Hall of India (2009)
Instructor bio
Prof. Ishapathik Das
IIT Tirupati
Prof. Ishapathik Das is an Professor in the Department of Mathematics and Statistics , IIT Tirupati . He did Postdoctoral Research Associate, Duke University, USA.Ph.D, Indian Institute of Technology Bombay, India. M.Sc, Indian Institute of Technology Kharagpur, India. B.Sc, Ramakrishna Mission Vidyamandira, Belur, India.
Course certificate
The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres. The exam is optional for a fee of Rs 1000/- (Rupees one thousand only). Date and Time of Exams: 27 October 2024 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm. Registration url: Announcements will be made when the registration form is open for registrations. The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then. Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.
CRITERIA TO GET A CERTIFICATE
Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course. Exam score = 75% of the proctored certification exam score out of 100
Final score = Average assignment score + Exam score
YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.
Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Tirupati. It will be e-verifiable at nptel.ac.in/noc.
Only the e-certificate will be made available. Hard copies will not be dispatched.
Once again, thanks for your interest in our online courses and certification. Happy learning.
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