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Math Help - Probability Mass Function Help!

  1. #1
    Junior Member Ruichan's Avatar
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    Probability Mass Function Help!

    The random variable X has pmf pX(x) = (1/2)^x+1, for x = 0,1,···. Find the probability that X is odd.

    This is the question. Please kindly help. I have no idea as to how to go about it.

    Thank you very much.

    URGENT!!! PLEASE HELP!!
    Last edited by Ruichan; October 17th 2006 at 11:21 PM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Ruichan View Post
    The random variable X has pmf pX(x) = (1/2)^x+1, for x = 0,1,···. Find the probability that X is odd.

    This is the question. Please kindly help. I have no idea as to how to go about it.

    Thank you very much.

    URGENT!!! PLEASE HELP!!
    The probability that X is odd is the sum of the mass function over all odd integers which is:

    sum(k=0..infty) pX(2k+1) = sum(k=0..infty) (1/2)^(2k+2)

    ..................................= sum(k=0..infty) (1/4)^(k+1)

    which is a geometric series which sums to 1/3.

    RonL
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  3. #3
    Junior Member Ruichan's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    The probability that X is odd is the sum of the mass function over all odd integers which is:

    sum(k=0..infty) pX(2k+1) = sum(k=0..infty) (1/2)^(2k+2)

    ..................................= sum(k=0..infty) (1/4)^(k+1)

    which is a geometric series which sums to 1/3.

    RonL
    Thank you very much.
    I'm just wondering if there's a way to solve it without using the geometric series? My prof hasn't gone into solving it via geometric series hence he doesn't want us to solve it any other ways except the very basic steps he taught us.
    I'm kind of slow when it comes to Math. Sorry if I sounded as if I don't know what I'm talking about.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Ruichan View Post
    Thank you very much.
    I'm just wondering if there's a way to solve it without using the geometric series? My prof hasn't gone into solving it via geometric series hence he doesn't want us to solve it any other ways except the very basic steps he taught us.
    I'm kind of slow when it comes to Math. Sorry if I sounded as if I don't know what I'm talking about.
    Look at the prbability the X is even:

    Pr(X even) = sum(k=0..infty) pX(2k+1) = 2 sum(k=0..infty) (1/2)^(2k+2) = 2 Pr(X odd)

    So we can see that Pr(X even)=2 Pr(X odd), but these two must sum to 1,
    so Pr(X even)=2/3 and Pr(X odd)=1/3.

    RonL
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