Re: Advanced Random Walk Question (bruce, pzhon)
The answer is about right, but there's a simpler and more accurate way to get it.
The reflection principle for a discrete random walk tells us to add the probability that the random walk is exactly 50 at the end of 1,000 steps to twice the probability that it is greater than 50. The continuous version is simpler, because the probability of being exactly 50 is zero.
Let s = SQRT(1,000) = 31.62.
The probability of being greater than 50 after 1,000 steps is approximately: N(-50.5/s) = 0.0551. The probability of being equal to 50 after 1,000 steps is approximately N(-49.5/2) - N(-50.5/2) = 0.0036. 0.0036 + 2*0.0551 = 0.1139.
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