Results 1 to 3 of 3

Thread: How many times do I need to subsample to sample all?

  1. #1
    Newbie
    Joined
    Jun 2019
    From
    Idaho
    Posts
    2

    How many times do I need to subsample to sample all?

    Lets say I have 10 million unique balls and I plan to subsample 1 million of the balls without replacement multiple times. Each time I go to subsample 1 million new balls, however, the balls will be replaced. How many times do I need to subsample the have subsampled all 10 million of the unique balls?
    Last edited by yahoo123; Jun 15th 2019 at 07:04 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Walagaster's Avatar
    Joined
    Apr 2018
    From
    Tempe, AZ
    Posts
    209
    Thanks
    139

    Re: How many times do I need to subsample to sample all?

    Quote Originally Posted by yahoo123 View Post
    Lets say I have 10 million unique balls and I plan to subsample 1 million of the balls without replacement multiple times. Each time I go to subsample 1 million new balls, however, the balls will be replaced. How many times do I need to subsample the have subsampled all 10 million of the unique balls?
    You can't give a certain answer to that. Say you have $n$ balls and select $k$ each time. Think of a particular ball, say the only red ball in the batch. The number of ways to miss the red ball in your sample is $\binom {n-1} k$. So after $m$ samples, the probablility of missing the red ball every time is $\left( \frac {\binom {n-1} k}{\binom n k}\right ) ^m$, which may be very small but not zero. To look at an example with smaller numbers, say $n=5$ and you sample $k = 1$ ball each time. The probablility of missing the red ball each time is $\frac 4 5$. After m trials the probablility of not having drawn the red ball is $\left( \frac 4 5\right) ^ m$. That number is never zero so there no number of trials that will guarantee success.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2019
    From
    Idaho
    Posts
    2

    Re: How many times do I need to subsample to sample all?

    Thank you!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: Feb 17th 2014, 05:08 PM
  2. Using auto-correlation to subsample
    Posted in the Statistics Forum
    Replies: 5
    Last Post: Feb 26th 2013, 03:04 PM
  3. Flip a weighted coin n times, flip again another n times
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: Oct 4th 2012, 01:34 PM
  4. Replies: 2
    Last Post: May 29th 2009, 09:32 AM
  5. Replies: 2
    Last Post: Dec 9th 2007, 02:33 PM

Search Tags


/mathhelpforum @mathhelpforum