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Math Help - Stats question (random variables)

  1. #1
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    Stats question (random variables)

    Suppose X and Y are independent random variables with X ~ N(6,2square) and Y ~ N(4,4square) Put D = Y -X

    (i) What is the probability distribution of D?
    (ii) Using you answer to (i) above or otherwise, evaluate P(Y<X)

    My answer for (i) D ~ N(-2,12)

    I am not sure if its correct, so please help!
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  2. #2
    MHF Contributor matheagle's Avatar
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    I'm not sure what you mean by 2 squared

    V(Y-X)=V(Y)+V(X)

    Then in part 2 use D=Y-X, so you want P(D>0)
    which you compute by standardizing D and using your N(0,1) tables.
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  3. #3
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    I am not really sure how to put the little 2 here.

    What i meant is two square and four square.
    So basically, it is N(6,4) and N(4,16)
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  4. #4
    MHF Contributor matheagle's Avatar
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    Most people write N(mean, variance)
    some write N(mean, st deviation).

    Your variance is 4+16=20

    P(D>0)=P\biggl({D-(-2)\over \sqrt{20}}>{0+2\over \sqrt{20}}\biggr)

    =P\biggl(Z>{2\over \sqrt{20}}\biggr)
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  5. #5
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    Hi thanks for the reply. Just to confirm, D should be N(10,20) then?

    I still don't really get how to do the second part.
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  6. #6
    MHF Contributor matheagle's Avatar
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    no, your mean was right the first time, -2 not 10.
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