Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Randomness and probability

  1. Oct 17, 2006 #1
    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
     
  2. jcsd
  3. Oct 18, 2006 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    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".)
     
    Last edited: Oct 21, 2006
  4. Oct 18, 2006 #3
    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
     
  5. Oct 20, 2006 #4

    CRGreathouse

    User Avatar
    Science Advisor
    Homework Helper

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Randomness and probability
  1. True randomness (Replies: 2)

  2. Randomness of pi (Replies: 24)

Loading...