Statistics

Different topics and problems in statistics and probability:

a_combination_problem.ipynb

Problem Statement

Anita randomly picks 4 cards from a deck of 52-cards and places them back into the deck (Any set of 4 cards is equally likely). Then, Babita randomly chooses 8 cards out of the same deck (Any set of 8 cards is equally likely). Assume that the choice of 4 cards by Anita and the choice of 8 cards by Babita are independent. What is the probability that all 4 cards chosen by Anita are in the set of 8 cards chosen by Babita?

Solutions

Two solution methods are suggested:

(i) Monte Carlo simulation, and 
(ii) Exact method

t_distribution.ipynb

Topic 1

Show how t-distribution converges to normal distribution

Topic 2

Use Monte Carlo Integration to estimate the CDF of a t-distribution at point a.

Confirm the results using the inverse of CDF function: PPF

forward_selection_with_statsmodel.py

Topic

Perform forward stepwise feature selection to narrow down predictors (a.k.a. features, or independent variables) in linear regression

Use k-fold cross-validation method and Root Mean Squared Error (RMSE) for evaluating and choosing regression models.

birthday.ipynb

Topic

Probablity that two persons in a group are born on the same day.