An unexpected result involving sums of random numbers
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03-01-2023, 03:54 AM
Post: #5
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RE: An unexpected result involving sums of random numbers
(02-28-2023 11:08 PM)Namir Wrote: The answer is a squewed distribution (Gauss, or Poisson, or something else?). Hi, Namir, Perhaps my phrasing was not so clear. Let’s do an example by hand on the HP-15C, step by step: 0 STO RAN#; start the sequence of random numbers with zero 1) f RAN# -> 0.1018 f RAN# -> 0.7365 + -> 0.8383 ; sum < 1, go on: f RAN# -> 0.3248 + -> 1.1631 ; sum >= 1 obtained with 3 random numbers. 2) f RAN# -> 0.3485 f RAN# -> 0.8685 + -> 1.2171 ; sum >= 1 obtained with 2 random numbers. 3) f RAN# -> 0.2789 f RAN# -> 0.3615 + -> 0.6404 ; sum < 1, go on: f RAN# -> 0.1074 + -> 0.7448 ; sum still < 1, go on: f RAN# -> 0.2629 + -> 1.0106 ; sum >= 1 obtained with 4 random numbers. 4) f RAN# -> 0.9252 f RAN# -> 0.5599 + -> 1.4851 ; sum >= 1 obtained with 2 random numbers. Average: (3 + 2 + 4 + 2)/4 = 2.75 That’s exactly what we get when running the program: 0 STO RAN# 4 f A -> 2.7500 The result, 2.75, is close to the constant we’re looking for. I thought of providing an HP-41C program, but then I remembered it lacks a random number generator. Gerson. |
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