Results 1 to 6 of 6

Math Help - statistics question

  1. #1
    Member
    Joined
    Sep 2008
    Posts
    76

    statistics question

    The general form for the pmf of X = number of children born upto and including the first boy is

    p(x) = p * (1-p)^(x-1) where x = 1,2,3,/......

    and p(x) = 0 otherwise

    find the expected value E(X).

    Okay,so this is an example from the book.But what I dont really get is why are they differentiating the p(x) inside the summation.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Jan 2009
    Posts
    94
    I'd be surprised if they are really differentiating. This is a discrete distribution. Would you please do the following?

    E(x) = sum x*p(x) = sum x*p * (1-p)^(x-1)
    = p sum x*(1-p)^(x-1)

    To compute sum x*(1-p)^(x-1). Let A=sum x*(1-p)^(x-1)
    write x*A/(1-p) and subtruct it from A.

    I mean write: x*A/(1-p) - A

    Do you see any terms canceling each other? There should be many.
    If you can't see, write them in two different lines, and let the same terms (x, x^2, x^2,...) come one top of another and see how they cancel each other.

    Good luck.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by NidhiS View Post
    The general form for the pmf of X = number of children born upto and including the first boy is

    p(x) = p * (1-p)^(x-1) where x = 1,2,3,/......

    and p(x) = 0 otherwise

    find the expected value E(X).

    Okay,so this is an example from the book.But what I dont really get is why are they differentiating the p(x) inside the summation.
    For |r| < 1 you should know (infinite geometric series) that

    S = \sum_{x=1}^{+\infty} r^x = \frac{r}{1-r} .... (1)


    Differentiate equation (1) with respect to r: \frac{dS}{dr} = \sum_{x=1}^{+\infty} x r^{x-1} = \frac{1}{(1-r)^2} .... (2)


    E(X) = \sum_{x=1}^{+\infty} x p (1 - p)^{x-1} =  p \sum_{x=1}^{+\infty} x (1 - p)^{x-1}.


    Now let r = 1 - p and use equation (1) to evaluate the sum in this expected value.
    Last edited by mr fantastic; February 28th 2009 at 11:20 PM. Reason: Fixed a typo
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Jan 2009
    Posts
    94
    Differentiate equation (1) with respect to x
    must be:
    Differentiate equation (1) with respect to r.

    <br />
\frac{dS}{dr} = \sum_{x=1}^{+\infty} x r^{x-1} = \frac{1}{(1-r)^2}<br />

    -O
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by oswaldo View Post
    Differentiate equation (1) with respect to x
    must be:
    Differentiate equation (1) with respect to r.

    <br />
\frac{dS}{dr} = \sum_{x=1}^{+\infty} x r^{x-1} = \frac{1}{(1-r)^2}<br />

    -O
    Aw rats! The deliberate mistake I always make to see if the OP thinks about and understands what I post has been exposed. Second time this week it's happened, dran it. Now I gotta go fix it and put in a new mistake ....
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Sep 2008
    Posts
    76
    Why did you guys differentiate it ..that was my question initially

    okay,I see what's happening...thanks!
    Last edited by mr fantastic; March 1st 2009 at 11:11 AM. Reason: Merged posts
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. statistics question
    Posted in the Statistics Forum
    Replies: 5
    Last Post: December 2nd 2010, 04:06 AM
  2. Question about Statistics?
    Posted in the Statistics Forum
    Replies: 0
    Last Post: May 18th 2010, 07:23 PM
  3. Statistics question
    Posted in the Statistics Forum
    Replies: 1
    Last Post: March 20th 2009, 08:27 AM
  4. Statistics Question
    Posted in the Statistics Forum
    Replies: 4
    Last Post: February 27th 2009, 03:00 PM
  5. Statistics Question
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: March 24th 2007, 05:03 PM

Search Tags


/mathhelpforum @mathhelpforum