this is such a fun book to go through and i'd be happy to take a recreational course in it :)

#iTeachMath #MathSky

you can also see how the average size of the largest piece drops as the number of cuts increases

you can also ask questions about the distribution of resources

there are ways to change the how we cut [this graph assumed pulling from a Gamma(1,1)]

all told, it's a fun exploration

#math #mtbos

Here's a distribution of the largest cut as a percentage of the string. Interestingly, it's not too crazy to see the largest piece be 25% of the string even if we were targeting an average length of 5% (1/20). In fact, seeing the largest size to be near 5% is more unusual than 25%.

#math 🧵

You have to get into the Dirichlet distribution to make this work [there are other methods]. In any case, without going to much into the weeds, here's an image of 40 pieces of string, each cut into 20 pieces at random [and each string is sorted from smallest cut to largest].

#math 🧵

continued fraction expression of pi is fun

some other #piday math fun facts

mathmisery.com/wp/2019/03/1...

but if we remain open to the possibility that perhaps, just maybe, conversion rates don't improve, but in fact could get worse, then we allow ourselves to model the behavior differently

and indeed, we find a better parametric fit

#DataScience #MachineLearning #iTeachMath #MTBoS

If the unchallenged narrative is "more actions, better conversion", then we might be primed to model this via a monotonically increasing function and accept the disconnect between observation and fit, chalking it up to "low sampling volume"

#datascience #machinelearning #MathSky #MTBoS #iTeachMath

Unchallenged narratives influence the manner in which data is analyzed. It's common sense that the more a user engages with the product, the more likely they are to convert. But up to a point.

mathmisery.com/wp/2024/02/2...

#datascience #machinelearning #MathSky #MTBoS #iTeachMath

Love and Principal Component Analysis

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#ITeachMath #MTBoS #DataScience

There are two internal adversaries that will grind progress to a halt.

These are
- time
- other people's assumptions

Time management woes are habit woes. Other people's assumptions woes are culture woes. Our management of these depends on the empathy we have

mathmisery.com/wp/2023/12/0...

What I’ve found over the years between teaching stats courses and also working in industry across all business segments is that there is a disconnect between the correlation value, what that data looks like, and what a line of best fit can do.

#edusky #math

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Thinking about relationships in user engagement data

mathmisery.com/wp/2023/08/0...

#analytics #datascience #productmanagement

Ok, let's try it out over here and see how things go!

Wrote this up about game design for collectible type awards and the Geometric Distribution

mathmisery.com/wp/2023/09/1...

Do we use hashtags here?

#gamedesign #gaming #statistics