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Math Help - Distribution Functions

  1. #1
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    Distribution Functions

    Let X and Y be independent and identicall distributed random variables. Denote their common probability distribution function by F and denote their common density function by f. If

    V = max{X,Y} and U = min{X,Y}

    1.Express the distribution function of V in terms of F and f.

    Hint: Begin with Fv(v) = P[V<=v]

    2. Express the distribution function of U in terms of F and f.
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  2. #2
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    Note that if V < v, both X and Y must be less than v.

     F_v(v) = P(V \leq v) = P(X \leq v, Y \leq v) = P(X \leq v) P(Y \leq v) =\left[ F(v)\right]^2

    Do the same for U. (begin with P(U > u))
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  3. #3
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    Thanks, for that

    so does that mean that its
    F(u) = P(U>u) = P(X>u, Y>u) = P(X>u)P(Y>u) = [f(u)]^2
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  4. #4
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    No. The cumulative distribution function  F(u) is defined as  P(U \leq u) .
    Note that, since P is a probability,  P(U > u) + P(U \leq u) = 1 .

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