4 min read
Introducing Nova Pinball and Island Flight
The blog now has a Games page with two original browser games. Nova Pinball is a pinball table with an observatory theme, and Island Flight is a small-plane course over nine real cities.
Nad Am
Notes on mathematics, statistics and programming.
Latest posts
1 min read
A simple math identity about one
In this blog post, we will dive into how we can prove multiply b and c divided by product of a minus b and a minus c plus ... is equal to one.
4 min read
Introduction to Terraform to Host a Static Webpage
In this blog post, we will dive into how we can set up terraform for static website deployment.
2 min read
Proofs of Two Inequalities Involving Positive Integers and Non-negative Numbers
Proof of (a+b+c)/3 is greater than or equal to ((a^2+b^2+c^2)/3)^(1/5) and Schur's inequality
3 min read
Mixed Poisson Distribution With An Inverse Gaussian
The content provided is a mathematical derivation showing that a mixed Poisson distribution with an inverse Gaussian mixing distribution is equivalent to a Poisson-ETNB distribution.
2 min read
P-adic number computation
The given algorithm is a recursive implementation of the p-adic expansion.
2 min read
Inequality Around sum of the cubics and AM-GM variance
The given text consists of two parts. The first part contains two examples along with their proofs concerning inequalities. In the first example, it is proved that if 'a_i' are real numbers such that the sum of their squares, the summation of (a_i^2), is less than or equal to 4, then the sum of their cubes, the summation of (a_i^3), will be less than or equal to 8. The proof involves utilizing the AM-GM inequality to demonstrate that the sum of the cubes is bounded by 8. In the second example, an inequality is proved for non-negative numbers 'a', 'b', and 'c': a^3 + b^3 + c^3 - 3abc is greater than or equal to 2((b+c)/2 - a)^3.
3 min read
Achieving Non-Decreasing Array with Limited Operations and Constraints (50)
To make the given array non-decreasing, we can perform a maximum of 50 operations. If the array contains only non-positive numbers, we can use a simple approach of repeatedly adding consecutive elements from the end until the beginning of the array. This ensures that the array becomes non-decreasing within the operation limit.
7 min read
Introduction to different moments of distributions (Planned)
We will get into how to get different moments of different distributions and possible skewness and kurtosis of different distributions. We will also discuss the relationship between different moments and the moment generating function.
16 min read
A Brief Introduction to Compound Distributions (Part One)
The provided text discusses the concept of compound distributions, which arise when combining two independent distributions. The probability generating function (pgf) of a compound distribution is shown to be the composition of the pgfs of the primary and secondary distributions. Some of the examples are excerpted from Loss Model (Sixth Edition).