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Math Help - Mathematical statistics: two-dimensional random variables

  1. #1
    Newbie LaraSoft's Avatar
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    Mathematical statistics: two-dimensional random variables

    Boys, help a "blonde" to decide a task, please. I was tangled and does not know as correct to decide this task .

    The two-dimensional random variable (X,Y) has a function of probability density f\left( {x,y} \right) = \frac{a}<br />
{{{\pi ^3}\left( {{x^2} + 3{y^2} + {x^2}{y^2} + 3} \right)}}.
    Find
    a) the parametr a;
    b) the function of a distribution F\left( {x,y} \right);
    c) the probability of hit of a casual point \left( {X,Y} \right) in a square which is limited straight: x=0, y=0, x=1, y=1.
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  2. #2
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    Quote Originally Posted by LaraSoft View Post
    Boys, help a "blonde" to decide a task, please. I was tangled and does not know as correct to decide this task .

    The two-dimensional random variable (X,Y) has a function of probability density f\left( {x,y} \right) = \frac{a}<br />
{{{\pi ^3}\left( {{x^2} + 3{y^2} + {x^2}{y^2} + 3} \right)}}.
    Find
    a) the parametr a;
    The requirement is that the integral over the entire plane,
    \int_{x=-\infty}^\infty\int_{y=-\infty}^\infty f(x,y)dydx= 1
    choose a so that integral is equal to one.

    b) the function of a distribution F\left( {x,y} \right);
    Okay, that is equal to the indefinite integral
    \int\int f(x,y)dydx

    c) the probability of hit of a casual point \left( {X,Y} \right) in a square which is limited straight: x=0, y=0, x=1, y=1.
    \int_0^1\int_0^1 f(x,y) dy dx
    Last edited by mr fantastic; January 7th 2009 at 02:45 PM. Reason: Fixed a quote environment
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