This is the course webpage for the course 'Introduction to Probability and Statistics', PGP 2025-27 batch, Sections A & B
Session 1 - 2: Introduction to ProbabilityÂ
-- Random experiment, sample space, mutually exclusive and exhaustive events, classical definition of probability, some basic results on probability, long-run relative frequencies, conditional probability and associated results, independence of events.
Session 3: Joint Probability Distribution and Bayes' theorem
-- Joint probabilities and conditional probabilities, Bayes' theorem and its applications
Session 4 - 5: Random Variables
-- Random variables, Discrete Random variables, Probability Mass Function, Distribution Function, Expectation and Variance.
Session 6: Binomial and Poisson distributions
-- Introduction to Binomial and Poisson distributions, properties including expectation and variance.
Session 7: Continuous random variables
-- Introduction to continuous random variables, pdf, cdf, expectation, and variance.
Session 8: Uniform and Exponential Random variables
-- Introduction to Uniform and Exponential distributions, cdf, expectation, and variance, memoryless property of exponential, connection between exponential and Poisson random variables.
Sessions 9 - 10: The Normal distribution
-- Introduction to the Normal distribution, pdf, cdf, expectation, variance, standard normal distribution, percentiles.
Session 11: Bivariate Random variables, Conditional distributions, conditional expectation, and variance
-- Joint distribution of bivariate random variables, marginal and conditional distributions, expectation, variance, covariance, and correlation, linear combination of random variables with applications.
Session 12 - 13: Sampling Techniques, Sampling Distributions, Central Limit Theorem
-- Sampling techniques, Random samples, Concept of parameter and statistic, Sampling distribution of a statistic, Concept of large samples and CLT, sampling distribution of sample proportion, concept of standard error of a statistic.
Notes on Chi-squared, t, and F distributions
Session 14 - 15: Point Estimation, Interval estimation
-- Concept of unbiased estimator, Method of moments, Confidence intervals
Sessions 16 - 17: Hypothesis testing
-- Introduction to testing of hypothesis, null and alternate hypotheses, Type-I and Type-II errors, testing Normal mean and population proportion
Sessions 18 - 20: Hypothesis testing for two independent populations
-- Comparing means for two independent Normal populations, comparing two population proportions, Welch t-test and Pooled t-test, test of two proportions
People vs Collins [Session 3+]
The Curious Campaign at Lit Lane [Session 3+]
On-Time Logistics [Session 7+]
Waiting for a ride with ZippGo [Session 8+]
QuickAid Diagnostics [Session 8+]
CoolChurn [Session 9+]
Sienna Capital [Session 12+]
AeroVista [Session 14+]
Problem Set 1 [Total probability, Conditional probability]
Problem Set 2 [Binomial and Poisson distributions]
Problem Set 3 [Exponential distribution, Poisson process]
Problem Set 4 [Normal, CLT]
Problem Set 5 [Joint probability distributions, conditional expectation]
Problem Set 6 [Point estimation]
Problem Set 7 [Interval estimation]
Problem Set 8 [Testing of Hypothesis; single population]
Problem Set 9 [Testing of Hypothesis; two populations]
Problem Set 10 [More problems on Testing of Hypothesis for two populations]
Details of the assignment are in the file.
Submit detailed proposal of the survey by August 26, 2025. Details must inlcude the survey proposed, along with the questionnaire. Also include the ethical aspects mentioned in the assignment details.
Last date for submission is September 24, 2025. No date change requests shall be entertained.
Please mention if you have used GenAI in completing your assignment.
Submission through Google Forms (will be shared) only; no email/hardcopy submissions allowed.