## Insight Things

### A scientific blog revealing the hidden links which shape our world

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Quick question: Is BASF’s day-to-day rate of stock returns (shown below) distributed normally?

Day-to-day rates of return of BASF stock

Yes? In theory it isn’t! In theory rates of stock returns follow a lognormal distribution as I have shown in “On the distribution of stock return”. Unfortunately, most people don’t take the lognormal distribution serious, although it is very often at work! This article shows how the lognormal distribution arises and why its shape sometimes mistaken for a normal distribution. more →

This blog uses Custom Content by Country (by iControlWP) to localize content. However, my tests with geopeeker.com were disappointing. The result was always U. S. related instead of the countries the servers were actually situated in. It turned out that it’s not a matter of the plugin itself (it’s fantastic!), but the data on IPs and countries is weak. The good thing is that I could increase accuracy by replacing the IP data with those from ip2location. Here is how I achieved it! more →

There are many applications for the arc length of functions. I came across it when I needed to calculate the length of a density function in an interval $[a,b]$. The formula reads

$\displaystyle s=\int\limits_{a}^{b}\sqrt{1+\big[f'(x)\big]^{2}}\,dx$

Do you grasp how this formula arises? No? Let me show you! more →

One of statistic’s foundations lies in the fact you can add variances. Maybe you wonder a little bit, because the formula for the variance does not look like that at first glance. This article will show you the proof why and under which circumstances adding variances is a valid practice. Please check the information given in my articles on addition and multiplication of expected values, if you do not have collected experiences with it yet. more →

Are you also annoyed when it comes to parking your car? I asked myself, whether marked parking spots are rather hurdles than helpers, and wrote this article 🙂 The goal is to investigate what’s better: Marked or unmarked parking space? more →

Back in 2010, I visited a casino for the first time with some of my friends. I suggested to try a roulette strategy which I heard about earlier. It advices to “double stakes”. We earned almost 30 bucks within an hour. Let me explain what we did! more →

I’ve already explained in a demonstrative way how the formula for sum squared numbers arises. Not only will I only show in this article how to calculate simple series like 1+2+3+4+…., but you will also see how we enhance our findings to tackle more complicated series like 1³+2³+3³+…. These formulas are applied in many different contexts. more →

Have you ever wondered how the formula for the sum of squares (1+4+9+16+25+…) arises? Then this article is for you! We will see that there is a geometric interpretation for the problem of adding squared numbers. This interpretation will lead to the well-known formula (see “Sum of Squares, Cubes and Higher Powers” for higher powers). Curious? Then don’t let us waste time but start! more →