“Independent” does not mean “unrelated in spirit.” It means: knowing one outcome tells you nothing about the other. Dice rolls? Independent. Midterms and sleep? Probably not. Don’t confuse mutually exclusive (can’t both happen) with independent (don’t inform each other). If events are mutually exclusive and both have positive probability, they are not independent. Start with […]
Independence Isn’t Friendship Read More »
A probability isn’t a prediction; it’s a contract about the long run. “Thirty percent rain” means: if you could replay today a thousand times, it would rain in about 300 of them. On any single day, reality is lumpy. Act like a portfolio manager: define the sample space, list outcomes, assign fair odds, and make
Probability Is a Contract, Not a Crystal Ball Read More »
Two very different clouds can share the same correlation. One may be tight with a rebel; the other, loose but clean. Numbers rhyme; pictures speak. That’s why Anscombe’s lesson endures: always sketch the data. Write one sentence for each plot: direction, form, strength, outliers… and only then compute r. If your sentence and your statistic
Same r, Different Story Read More »
