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Math Help - Consider two random variables X and Y with the PMFs

  1. #1
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    Consider two random variables X and Y with the PMFs

    Consider two random variables X and Y with the PMFs
    pX(x) =
    (
    1/10 + a(x − 5)2, if x 2 {3, 4, 5, 6, 7}
    0, o.w.
    ,
    pY (y) =
    (
    3/10 − b(y − 3)2, if y 2 {1, 2, 3, 4, 5}
    0, o.w.
    .
    (a) Find a and b.
    (b) Evaluate 2X
    and 2Y
    . Which one is larger? Explain how you would reach the
    same answer without calculating the variances.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by sadasoria View Post
    Consider two random variables X and Y with the PMFs
    pX(x) =
    (
    1/10 + a(x − 5)2, if x 2 {3, 4, 5, 6, 7}
    0, o.w.
    ,
    pY (y) =
    (
    3/10 − b(y − 3)2, if y 2 {1, 2, 3, 4, 5}
    0, o.w.
    .
    (a) Find a and b.
    (b) Evaluate 2X
    and 2Y
    . Which one is larger? Explain how you would reach the
    same answer without calculating the variances.
    Please try and improve the statement of the question, that is almost incomprehensible.

    To do part a) you need to use the result that for a random variable U:

    \sum p_U(u) =1

    (the sum of the probabilities of all the possible outcomes is 1)

    CB
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