Connections Puzzle #523 🟪🟪🟪🟪 🟨🟨🟨🟨 🟦🟦🟦🟦 🟩🟩🟩🟩

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Strands #211 “Words with weight” 💡🔵🔵🔵 🔵🔵🔵🔵 🟡

Might be my first one with just a single hint!

I might have made this up as well, but I have a very distinct memory of basically suddenly becoming conscious at around being 3 years old. I woke up from a nap and for a couple hours or possibly days, I wasn’t sure whether I was dreaming or the world around me was actually real. After a couple of days of waking up in the same environment, I eventually accepted this to be reality. I of course don’t remember everything from this point on in my life, but it really felt like the first time I was able to explicitly think about stuff.

I didn’t see the pattern either and had to look it up. Apparently, you can rewrite 1 + 1/(1+2) + 1/(1+2+3)+… as 2(1 - 1/2 + 1/2 - 1/3 +…+1/n - 1/(n + 1)) = 2(1 - 1/(n + 1))

From there, the limit of 2 is obvious, but I guess you just have to build up intuition with infinite sums to see the reformulation.

The t-distribution approaches the normal distribution with increasing degrees of freedom. It is certainly more relevant in for example hypothesis testing, since t-Tests (variance is estimated from the data) is much more common than z-tests (variance is treated as fixed and coming from a normal distribution).

In all of statistics or probability theory, the normal theory is however way more influential.

Nonetheless, it’s a cool bit of history where modern statistics got its roots. As a lover of both statistics and guinness, i approve!🍻