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    Probability density function

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    ) Let X and Y have joint probability density function f(x,y) (s,t) = ce ^ -(s + 2t) for
    0 <= s, and 0 <= t. Find
    (a) c
    (b) Pr {min (X, Y) 1/3}
    (c) Pr {X <= Y}
    (d) The marginal probability density function of X
    (e) E [XY]

    5) Let X and Y be independent uniform (0,1) random variables. Compute
    (a) Pr {X < Y}
    (b) Pr {X = Y}
    (c) The probability density function of X + Y
    (d) Var[X]
    (e) Var[X + Y]

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    Solution Preview


    a) We must have:



    b) I think that must be Pr{min(X, Y)<=1/3}. Then:

    c) Pr{X<=Y}:
    There are two methods for solving this problem.
    Method 1:

    Method 2:

    remember that s represents X and t represents Y.

    d) The ...

    Solution Summary

    Given a joint density function, this shows how to compute a marginal probability density function; given the type of variable, this shows how to compute probability density function.