Intro to Statistics and Computation with Data

Syllabus:

Prerequisites: Probability 1 or 2 should cover statements of Law of Large Numbers, Strong Law of Large Numbers, Binomial Central Limit Theorem and Central Limit Theorem.

i) R- Basics: Installing R, Variables, Functions, Workspace, External packages and Data Sets.
ii) Introduction to exploratory Data analysis using R: Descriptive statistics; Graphical representation of data: Histogram, Stem-leaf diagram, Box-plot; Visualizing categorical data.
iii) Review of Basic Probability: Basic distributions, properties; simulating samples from standard distributions using R commands.
iv) Sampling distributions based on normal populations: t, 2 and F distributions.
v) Model fitting and model checking: Basics of estimation, method of moments, Basics of testing including goodness of fit tests, interval estimation; Distribution theory for transformations of random vectors;
vi) Nonparametric tests: Sign test, Signed rank test,Wilcoxon-Mann-Whitney test.
vii) Bivariate data: covariance, correlation and least squares.
viii) Resampling methods: Jackknife and Bootstrap.

Reference Texts:

(a) John Verzani: Using R for Introductory Statistics.
(b) James McClave and Terry Sincich: Statistics.
(c) Deborah Nolan and Terry Speed: Stat Labs.
(d) John A. Rice: Mathematical Statistics and Data Analysis.

https://www.isibang.ac.in/~adean/infsys/database/Bmath/SCD.html