Thread: 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..

any ideas?

Originally Posted by zeubi94

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

Thanks for your answer but do you mind explaining by steps because i am actually stuck somewhere?!

Originally Posted by zeubi94

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.

Thanks but i should find 1/4 instead of 4 :s