Viliam_Bur comments on Jokes Thread - Less Wrong Discussion
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Um.
Probability of a head = 0.5 necessarily means that the expected number of heads in 1000 tosses is 500.
Probability of a head = 0.6 necessarily means that the expected number of heads in 1000 tosses is 600.
Are you playing with two different meanings of the word "expected" here?
If I roll a 6-sided die, the expected value is 3½.
But I don't really expect to see 3½ as an outcome of the roll. I expect to see either 1, or 2, or 3, or 4, or 5, or 6. But certainly not 3½.
If my model says that 0.2 coins are heads-only and 0.8 coins are fair, in 1000 flips I expect to see either 1000 heads (probability 0.2) or cca 500 heads (probability 0.8). But I don't expect to see cca 600 heads. Yet, the expected value of the number of heads in 1000 flips is 600.
No, I'm just using the word in the statistical-standard sense of "expected value".