As an aside, the second is close to a log-normal distribution, meaning its logarithm is normally distributed (binomial distributions are very close to normal in the limit of a large number of small steps). You can see this by saying that multiplying p by a or 1/a is the same as adding or subtracting log(a) from log(p).
Ohh cool! I was sort of wondering about that but I’ve only ever heard about the log-normal distribution (never really used it) and didn’t get around to looking into its relationship to this problem. Thanks for calling that out!
As an aside, the second is close to a log-normal distribution, meaning its logarithm is normally distributed (binomial distributions are very close to normal in the limit of a large number of small steps). You can see this by saying that multiplying p by a or 1/a is the same as adding or subtracting log(a) from log(p).
Ohh cool! I was sort of wondering about that but I’ve only ever heard about the log-normal distribution (never really used it) and didn’t get around to looking into its relationship to this problem. Thanks for calling that out!