Random Number Sequences and Probabilities: Are They All Equal?

[ValenceE]

Hello to all,

I have a question about probabilities applied to series…

How would you rate the probability that a sequence of numbers generated by a true random generator would be comprised of numbers that are part of the result of an equation such as a(n) = 2n+1, or any other one that would generate a series of numbers?

Do all number sequences generated by a true random generator have the same probability of coming out ?


Hope I'm clear enough on my formulation...

Regards,

VE

 

[HallsofIvy]

I think that question is too general to be answered. What types of equations are you talking about?

Yes, a true random number generator would produce all sequence, of a given length, with the same probability. In other words, it would be as likely to produce 1, 2, 3, 4, 5, as it would be to produce 2, 4, 6, 8, 10 or 7, 5, 1332, 3433, 234433, or any particular sequence that "looked" random. In other words, "looking random" is a very poor test of a random number generator.

(Added in edit: at first I said 'or any sequence that "looked random"' without the word "specific". Since there are many more sequences that "look random" than there are that "look regular", the probability of producing a sequence that "looks random" (as opposed to a specific such sequence) is much higher than the probability of producing a sequence that "looks regular".)

 

[ValenceE]

Thank’s for the reply

I ‘kinda expected that, as a mathematical fact, they would have the same probability of coming out…

You see, my original assumption was that if you take, let’s say, 100 non identical randomly generated numbers, reorganized in increasing order, and find them to be the same as 100 numbers that were a result of a ‘deterministic’ series equation, that the ‘odds’ or probability of that happening would have to be much smaller than any other randomly generated sequence of 100 numbers.

I guess the assumption could be about opposing randomness with determinism, or something to that effect…



VE

 

[CRGreathouse]

You see, my original assumption was that if you take, let’s say, 100 non identical randomly generated numbers, reorganized in increasing order, and find them to be the same as 100 numbers that were a result of a ‘deterministic’ series equation, that the ‘odds’ or probability of that happening would have to be much smaller than any other randomly generated sequence of 100 numbers.

If you have some sequence of 100 numbers ahead of time, it's easy enough to figure the chances you'll get exactly your sequence. If you are allowed to generate the sequence after seeing the random numbers, that doesn't mean much -- if nothing else you can fit a polynomial of degree 99 to the points.