Which envelope should you choose?
A detailed solution for a problem about total probability
Probability and Statistics
Probability and Statistics
Math, Probability and Statistics
Variance, Covariance, Autocovariance…what?
This article aims to distinguish between Variance, Covariance, Correlation, Autocovariance, and Autocorrelation. Furthermore there will be a numerical discrete example for computing the Autocorrelation in python. This article will not
Probability and Statistics
Understanding the Probability Density Function of the Normal Distribution
A random variable \(Z\) is said to have the standard normal distribution, if its probability density function (pdf) is as follows: \[\begin{equation}f_Z(z)=\frac{1}{\sqrt{2\pi}} * \exp(\frac{-z^2}{2}), \quad -\infty<z<\infty\end{equation} \tag{1}\label{eq:eq1} \] This formula
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: Binominal Distribution Example
https://gist.github.com/irene-markelic/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