1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Distribution of the decimals of a random number

  1. Jul 10, 2010 #1
    1. The problem statement, all variables and given/known data

    Let U = 0.X1X2X3... be a random number in (0,1].

    1) Find the distribution of every decimal digit Xi, i = 0,1,2...

    2) Show that they are independent of each other

    3. The attempt at a solution

    I could use a hint for N°2. I have an idea, but I think it's wrong:

    If X1 and X2 are independent, then P(X2 = x2 (intersection) X1 = x1) = P(X2 = x2)*P(X1 = x1).

    Since P(X2 = x2 (intersection) X1 = x1) = P(0.x1x2... < U <= 0.x1(x2+1)...) = 0.x1(x2+1) - 0.x1x2 = 0.01 = 0.1*0.1 = P(X2 = x2) * P(X1 = x1) , that should prove it. Then, I could invoke the induction principle. But something sounds off.

    Is this correct?
  2. jcsd
  3. Jul 11, 2010 #2
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Distribution of the decimals of a random number
  1. Random numbers (Replies: 2)