Which envelope should you choose?
A detailed solution for a problem about total probability
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
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: 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