Results 1 to 4 of 4

Math Help - Rolling 5 Die

  1. #1
    Super Member Aryth's Avatar
    Joined
    Feb 2007
    From
    USA
    Posts
    652
    Thanks
    2
    Awards
    1

    Rolling 5 Die

    Let a fair die be rolled 5 times. Find the math expectation of the product of the outcomes.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member apcalculus's Avatar
    Joined
    Apr 2009
    From
    Boston
    Posts
    293
    Quote Originally Posted by Aryth View Post
    Let a fair die be rolled 5 times. Find the math expectation of the product of the outcomes.
    If the outcomes are 1 1 1 1 1 then the product is 1 with a probability of \frac{1}{6^5}.

    A product of 2 could happen in 5 different ways, so the probability is \frac{5}{6^5}.

    Same probability applies to an outcome of 3 and 5.

    The largest out come is five 6s, which has a probability of \frac{1}{6^5}

    Hope this helps.

    Outcome Ways
    1 1
    2 5
    3 5
    4 5 + 10
    5 5
    6 5 + 10 + 10
    ...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Mar 2008
    Posts
    934
    Thanks
    33
    Awards
    1
    Quote Originally Posted by Aryth View Post
    Let a fair die be rolled 5 times. Find the math expectation of the product of the outcomes.
    Hi Aryth,

    Let's see if we can solve the corresponding problem for 2 dice. With luck, maybe this will show us the way to a more general solution.

    To that end, let's say x and y are the numbers on the two dice. We assume each pair (x,y) has equal probability, i.e. 1/36. By definition, the expected value of their product is

    E(XY) = \sum_{x,y} xy \; p(x,y)
     = \sum_{x=1}^6 \sum_{y=1}^6 \frac{xy}{36}
     = \frac{1}{36} \left( \sum_{x=1}^6 x \right) \left( \sum_{y=1}^6 y \right)
     = \frac{1}{36} \left( \frac{6 \cdot 7}{2} \right) ^2


    Maybe you can take it from there...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    Looks like... for k dice...

    \frac{1}{6^k} \left( \frac{6 \cdot 7}{2} \right) ^k

    which also works when k=1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. rolling
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: March 25th 2011, 10:11 PM
  2. Rolling Dice
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: June 18th 2010, 10:10 PM
  3. Replies: 0
    Last Post: December 29th 2009, 09:08 PM
  4. Rolling a die
    Posted in the Statistics Forum
    Replies: 3
    Last Post: November 2nd 2009, 07:53 AM
  5. rolling a die ...
    Posted in the Statistics Forum
    Replies: 1
    Last Post: August 25th 2007, 03:41 AM

Search Tags


/mathhelpforum @mathhelpforum