Module I
Probability theory: probability spaces, conditional
probability, independence – Random variables: discrete
and continuous random variables, functions of random
variables, generating random variables – Multivariate
random variables: joint distributions, independence,
generating multivariate random variables, rejection
sampling – Expectation: Mean, variance and covariance,
conditional expectation
Module II
Random process: definition, mean and autocovariance
functions, iid sequences, Gaussian and Poisson process
, random walk – Convergence of random process: types
of convergence, law of large numbers, Central limit
theorem, monte carlo simulation – Markov chains: recurrence,
periodicity, convergence, markovchain monte carlo
Gibbs sampling, EM algorithm, variational inference
Module III
Descriptive statistics: histogram, sample mean and variance,
order statistics, sample covariance, sample covariance
matrix – Frequentist statistics: sampling, mean square
error, consistency, confidence intervals, parametric
and nonparametric model estimation
Module IV
Bayesian statistics: Bayesian parametric models, conjugate
prior, bayesian estimators – Hypothesis testing: testing
framework, parametric testing, permutation test, multiple
testing – Mixture models: Gaussian mixture models, multinomial
mixture models
Module V
Linear regression: linear models, leastsquares estimation,
interval estimation in simple linear regression, overfitting
– Multiple linear regression models: Estimation of model
parameters, MLE – Non linear regression: Non linear
least squares, transformation to linear model – Generalized
linear models: logistic regression models, Poisson regression

1. Michael
Mitzenmacher and Eli Upfal; Probability and Computing,
2ed, Cambridge University
Press, 2017
2. Alan Agresti, Christine A. Franklin and Bernhard
Klingenberg; Statistics: The Art and Science of
Learning from Data, 4ed, Pearson, 2017
3. Sheldon M Ross; A First Course in Probability, 10ed,
Pearson, 2018
4. Robert V Hogg, Joseph W McKean and Allen T Cralg;
Introduction to Mathematical Statistics,
8ed, Pearson, 2018
5. Douglas C Montgomery, Elizabeth A Peck and G Geoffrey
Vining; Introduction to Linear
Regression Analysis, 5ed, WileyBlackwell, 2012
Online Resources:
Course notes of Carlos FernandezGranda, DSGA 1002:
Probability and Statistics for Data Science
https://cims.nyu.edu/~cfgranda/pages/DSGA1002_fall17/index.html
