Ask them to program the coin toss experiment. If your friends are computer programmers then I found that the easiest way to appeal to their intuition is through programming. He will not be making any adjustments to his expectations about the probability of the next head, and leave it at 0.5 So, the frequentist will conclude after long months of tossing a coin 1 million times and observing a 10-head combination, that it's no big deal, things happen. [Note for anyone thinking " is he talking about expected absolute difference or the RMS difference" - actually either: for large $n$ the first is $\sqrt\approx 1$$ It still has 0 expected value, but its expected distance from 0 grows as the square root of the number of time steps. If you think of a particle moving up or down the y-axis by a unit step (randomly with equal probability) at each time-step, then the distribution of the position of the particle will 'diffuse' away from 0 over time. The grey traces (representing $n_H-n_T$) are a Bernoulli random walk. Here's the result of 100 sets of 1000 tosses, with the grey traces showing the difference in number of head minus number of tails at every step. On average, imbalance between the count of heads and tails actually grows! The counts don't tend toward "balancing out". Suppose that we repeatedly toss a coin which is unfair in the sense that the probability of observing heads is p, and the probability of observing tails. That is, nothing acts to make them more even. If $n_H$ is the number of heads in $n=n_H+n_T$ tosses ($n_T$ is the number of tails), for a fair coin, $n_H/n_T$ will tend to 1, as $n_H+n_T$ goes to infinity. The Cincinnati Bengals successfully called heads (-105) as the opening toss and elected to kick. The 2022 Super Bowl 56 coin toss result was heads. it just goes on randomly being heads or tails with constant chance of a head. In Super Bowl 56, the Los Angeles Rams defeated the Cincinnati Bengals 23-20. It cannot know there was an excess of heads. If it's a fair coin, then it's still 50-50 at every toss.
There's only a "balancing out" in a very particular sense. They are trying to assert that if there have been 10 heads, then the next in the sequence will more likely be a tail because statistics says it will balance out in the end
0 kommentar(er)
