Binomial Coefficient
Complement: You can either choose a team of k members from a group of n people, or you choose all the n-k people from the group, that are NOT in […]
Math
Math
This is my extended brain for math
Probability and Statistics
Stars and Bars Argument (Einstein-Bose) or placing n identical objects into n distinct bins, or drawing k times from n balls with replacement, order does not matter
https://brilliant.org/wiki/integer-equations-star-and-bars/ https://brilliant.org/wiki/identical-objects-into-distinct-bins/ So, the total number of objects consists of the number of balls or start or else plus the number of bins -1 (which is the number of bars
Probability and Statistics
Jupyter-Notebook: Confirming frequentists interpretation of conditional dependency
AllGirlsIfAtLeastOneGirl In [6]: from scipy.stats import binom, uniform import numpy as np #sample from a binomial distribution #Model: Urn with balls of 2 colors. Draw a ball n times with replacement
Probability and Statistics
Jupyter-Notebook: Birthday-Problem
https://gist.github.com/sallos-cyber/92bc3666b6228925c5798dc296171ab3#file-birthdayexample-ipynb BirthdayExample How large is the probability that there are at least two people in a group of k people whose birthday is on the same day? Thus, the event
Probability and Statistics
Jupyter-Notebook: Binominal Distribution Example
https://gist.github.com/sallos-cyber/c57d616a1dab051b4d57e70d36fb920b#file-binomialdistributionexample-ipynb BinomialDistributionExample In [1]: from scipy.stats import binom import matplotlib.pyplot as plt # experiment: 10 balls, 7 are white and 3 black # we pick a ball 10 times with replacement