4 ms·
"fair coin" refers to both the probability of heads and tails being equal (which is still justified) as well as the trials being independent (unlikely with 100/
by dooglius 10mo ago
"fair coin" refers to both the probability of heads and tails being equal (which is still justified) as well as the trials being independent (unlikely with 100/200; more likely the "coin" is some imperfect PRNG in a loop)
- tshaddox 10mo ago> more likely the "coin" is some imperfect PRNG in a loop "More likely"? How can you even estimate the likelihood of the coin being "an imperfect PRNG" based on a single trial of 200 flips?
- ajuc 10mo agoBayesian vs frequentist in a nutshell :) If a student was tasked with determining some physical constant with an experiment and they got it exactly right to 20th decimal place - I'll check their data twice or thrice. Just saying. You continue believing it was the most likely value ;)
- dooglius 10mo agoYou can use combinatorics to calculate the likelihood. If your PRNG is in a cycle of length N in its state space (assuming N>200), and half the state space corresponds to heads (vs tails), then the likelihood would be (N/2 choose 100)^2/(N choose 200) versus your baseline likelihood (for a truly random coin) of (200 choose 100)/2^200. Graphing here https://www.wolframalpha.com/input?i=graph+%28%28N%2F2+choose+100%29%5E2%2F%28N+choose+200%29%29+and+%28%28200+choose+100%29%2F2%5E200%29+from+500+to+5000 https://www.wolframalpha.com/input?i=graph+%28%28N%2F2+choos... and it does look like it's only a slight improvement in likelihood, so I did overstate the claim. A more interesting case would be to look at some self-correcting physical process.