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Thread: random variables

  1. #1
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    random variables

    Given independent random variables X and Y with the following joint distribution. Find
    random variables-captura.jpg

    a ?
    b?
    Last edited by Amanda2018; Oct 25th 2018 at 12:33 AM.
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  2. #2
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    Re: random variables

    Quote Originally Posted by Amanda2018 View Post
    Given independent random variables X and Y with the following joint distribution. Find
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    a ?
    b?
    random variables-untitled6.gif
    I replaced the ? with letters $p~q~r~s$
    $ \begin{align*}b+p&=0.7 \\b+r&=a \\p+0.18&=s \\r+0.18&=q \\0.7+q&=\\a+s&=1 \end{align*}$

    You continue.
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  3. #3
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    Re: random variables

    0.7 + q = 1
    q = 0.3
    r + 0.18 = 0.3(q)
    r = 0.12

    a = b + 0.12
    b = 0.7 - p
    for get a,b value, how i can get 'p' value?
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  4. #4
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    Re: random variables

    Quote Originally Posted by Amanda2018 View Post
    0.7 + q = 1
    q = 0.3
    r + 0.18 = 0.3(q)
    r = 0.12

    a = b + 0.12
    b = 0.7 - p
    for get a,b value, how i can get 'p' value?
    Use the fact the variables are independent.
    $\mathcal{P}(X=1\cap Y=1)=\mathcal{P}(X=1)\cdot\mathcal{P}(Y=1)$
    Thanks from Amanda2018
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  5. #5
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    Re: random variables

    Thank!
    i work out: a = 0.4, b= 0.28
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