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Math Help - Discrete Random Variables - pmf

  1. #1
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    Discrete Random Variables - pmf

    The discrete random variable R takes the values in S = { -3, -1, 1, 3 } with probabilities respectively,

    ( 1 - theta )/4, ( 1 - 3theta) /4, ( 1 + 3theta)/4, (1+ theta)/4,

    where theta is a real constant. Find the range of values for which this is a valid probability mass function.

    i think the answer is -1/3 =< theta =< 1/3
    BUT HOW DO PROVE IT!!!!!!!

    help!!
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  2. #2
    Super Member ILikeSerena's Avatar
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    Re: Discrete Random Variables - pmf

    Quote Originally Posted by Matt1993 View Post
    The discrete random variable R takes the values in S = { -3, -1, 1, 3 } with probabilities respectively,

    ( 1 - theta )/4, ( 1 - 3theta) /4, ( 1 + 3theta)/4, (1+ theta)/4,

    where theta is a real constant. Find the range of values for which this is a valid probability mass function.

    i think the answer is -1/3 =< theta =< 1/3
    BUT HOW DO PROVE IT!!!!!!!

    help!!
    Hi Matt1993!

    What is the reason you think that -1/3 =< theta =< 1/3?
    That is likely the key to the proof...
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    Re: Discrete Random Variables - pmf

    See all I did was let the pmfs equal zero and then I just tried values until I came up with that answer. That's the problem
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  4. #4
    Super Member ILikeSerena's Avatar
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    Re: Discrete Random Variables - pmf

    Quote Originally Posted by Matt1993 View Post
    See all I did was let the pmfs equal zero and then I just tried values until I came up with that answer. That's the problem
    That's close.

    The axioms of probability (see wiki) require in particular 2 things from the probabilities:

    1. Each probability is at least 0: p \ge 0.
      .
    2. The sum of all probabilities is 1: \sum p = 1.



    In your case that means:

    ( 1 - \theta )/4 \ge 0

    ( 1 - 3\theta) /4 \ge 0

    ( 1 + 3\theta)/4 \ge 0

    (1+ \theta)/4 \ge 0

    ( 1 -\theta )/4 + ( 1 - 3\theta) /4 + ( 1 + 3\theta)/4 + (1+ \theta)/4 = 1
    Last edited by ILikeSerena; March 11th 2013 at 01:49 PM.
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