MA2L006
Undergraduate (BTech)
· Generally offered: Spring
Combinatorics, Probability and Statistics
L 3 T 1 P 0 Credits 4 Hours 4
b Fundamental techniques of enumeration and construction of combinatorial structures, pigeon-hole principle, permutation, combination, summations. Introduction to recurrence relation and generating function, principle of inclusion-exclusion
Probability: Classical and axiomatic definitions of probability, Addition rule and conditional probability, Multiplication rule, Bayes' Theorem and independence, Discrete and continuous random variables: Uniform, Binomial, Geometric, Poisson, Exponential, Gamma, Normal distributions etc, Jointly distributed random variables. Mathematical expectation, Moments, Probability- and Moment-generating functions, Chebyshev's inequality, the strong and weak law of large numbers, Functions of Random Variables and their probability distributions
Statistics: The Central Limit Theorem, Distributions of the sample mean and the sample variance for a normal population, Sampling Distributions: Chi-Square, t and F distributions, Point and interval Estimation, maximum likelihood estimation, Null and alternative hypotheses, The critical and acceptance regions, Neyman-Pearson Fundamental Lemma, Tests for one sample and two samples problems for normal populations.
Probability: Classical and axiomatic definitions of probability, Addition rule and conditional probability, Multiplication rule, Bayes' Theorem and independence, Discrete and continuous random variables: Uniform, Binomial, Geometric, Poisson, Exponential, Gamma, Normal distributions etc, Jointly distributed random variables. Mathematical expectation, Moments, Probability- and Moment-generating functions, Chebyshev's inequality, the strong and weak law of large numbers, Functions of Random Variables and their probability distributions
Statistics: The Central Limit Theorem, Distributions of the sample mean and the sample variance for a normal population, Sampling Distributions: Chi-Square, t and F distributions, Point and interval Estimation, maximum likelihood estimation, Null and alternative hypotheses, The critical and acceptance regions, Neyman-Pearson Fundamental Lemma, Tests for one sample and two samples problems for normal populations.
3 questions tagged to this course
4
Votes
Is a matrix populated randomly by 0/1 invertible?
Suppose each entry of a $2\times 2$ matrix is populated with $0$ or $1$ independently with probability $1/2$. What is the probability that this matrix invertible? What will be the …
0
Votes
Expected number of records in a random permutation of [n]
Working through $\mathbb{E}[R_n] = \sum_{k=1}^n \frac{1}{k} = H_n$ — simulation matches, want a cleaner indicator-variable writeup.