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Tag: expected value

Alternative formula for the mean

An often forgotten formula for the mean of a random variable $X$ is given by:

$\displaystyle \mu=E(X)=\sum_{x=0}^{\infty} \Big(1-F(x)\Big)$

And for the continous case:

$\displaystyle \mu=E(X)=\int_{x=0}^{\infty} \Big(1-F(x)\Big)$

This blog post is going to illustrate how these formulas arise.

Trapped: Division by means and expected values

June 25, 2016 / Jan Rothkegel / 1 Comment

It was really surprising for me when I thought about this kind of operation, namely division by arithmetic means and expected values. People tend to work with means and expected values very intuitively. You can add and multiply them without any issues. Dividing on the other hand can be misleading and I am going to illustrate this with some neat examples.

Why you can add variances

March 4, 2016 / Jan Rothkegel / 0 Comments

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 →

Double Stakes – Roulette with Martingale

March 2, 2016 / Jan Rothkegel / 0 Comments

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 →

Why you can multiply means and expected values

February 28, 2016 / Jan Rothkegel / 0 Comments

Maybe you had to multiply means or expected values already. If you know, for instance, how often people go shopping on average and how much money they spent on their shopping tours on average then you could multiply both to obtain the average amount spent. In this post I will explain why multiplying means and expected values is a valid operation. more →

Why you can add means and expected values

February 27, 2016 / Jan Rothkegel / 0 Comments

In applied statistics you often have to combine data from different samples or distributions. One of the most frequently used operation here is to add means and expected values. For instance, you could sample people’s leg length, body and head height. The result when adding these means? It is the average body height, I hope! more →