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Math Help - Double integration

  1. #1
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    Double integration

    Hello, do you mind helping me with this please?

    let for some a>0

    f(x,y) = a2(cos (x - y) + sin ( x + y)) 0 ≤ x π/2 and 0 ≤ y π/2

    Assume without computing a that f(x,y) is the p.d.f of a bivariate random variable ( X,Y) and compute the marginal p.d.f f1(x) and f2(y). Either from f1(x) or f,(y) find the value a > 0 such that f(x,y) is a proper p.d.f
    So i need to find a such as the function equals to 1.
    i should find 1/2 but i must have forgotten something..
    Last edited by zeubi94; December 12th 2012 at 02:40 PM.
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  2. #2
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    Re: Double integration

    any ideas?
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  3. #3
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    Re: Double integration

    Quote Originally Posted by zeubi94 View Post
    let for some a>0
    f(x,y) = a2(cos (x - y) + sin ( x + y)) 0 ≤ x π/2 and 0 ≤ y [COLOR=#000000][FONT=sans-serif]π/2
    \int_0^{\frac{\pi }{2}} {\int_0^{\frac{\pi }{2}} {\left[ {\cos \left( {x - y} \right) + \sin \left( {x + y} \right)} \right]dydx} }  = 4
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  4. #4
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    Re: Double integration

    Thanks for your answer but do you mind explaining by steps because i am actually stuck somewhere?!
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  5. #5
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    Re: Double integration

    Quote Originally Posted by zeubi94 View Post
    Thanks for your answer but do you mind explaining by steps because i am actually stuck somewhere?!
    Yes I do mind. But you can look at this page.
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  6. #6
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    Re: Double integration

    Thanks but i should find 1/4 instead of 4 :s
    Last edited by zeubi94; December 12th 2012 at 04:29 PM.
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