## Insight Things

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

#### Tag: 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.

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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.

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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 →

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 →