4 ms·
After careful consideration I've always enjoyed how: p(rain,coat) = p(rain) * p(coat | rain) Can be pronounced: "the probability of rain, and coat (wearin
by escherize 11y ago
After careful consideration I've always enjoyed how:
p(rain,coat) = p(rain) * p(coat | rain)
Can be pronounced: "the probability of rain, and coat (wearing) is the probability of rain times the probability of (my wearing a) coat given rain". This intuitively showcases how the order of independent events doesn't effect the outcome, since after all:
p(coat,rain) = p(rain,coat) = p(rain) * p(coat | rain)
- jsprogrammer 11y agoThe problem with that example is that there is no reason to assume that coat wearing and rain are independent (in fact, you have even modeled that wearing a coat is partially dependent on it raining). Maybe I missed your point?
- escherize 11y agoNo, you're right those events shouldn't be called independent! A defintition of independent events is: A and B are independent events iff P(A|B) = P(A) and P(B|A) = P(B) So that was just plain wrong.