Need help with Probability
Suppose that a point with co-ordinates (X,Y ) is chosen uniformly at random from the disc {(x,y) ∈ R2 : x2 + y2 ≤ 1}. Let random variables R ≥ 0 and Θ ∈ [0,2π) satisfy X = Rcos(Θ) and Y = Rsin(Θ).
(i) What is the joint p.d.f of X and Y ?
(ii) What are the marginal p.d.f s of X and Y ? Are X and Y independent?
I have no idea how to do this. Can anyone explain what I need to do please?
(i) What is the joint p.d.f of X and Y ?
(ii) What are the marginal p.d.f s of X and Y ? Are X and Y independent?
I have no idea how to do this. Can anyone explain what I need to do please?
Original post by pineapplechemist
Can anyone explain what I need to do please?
I would have simply said f(x,y)=1/"area of disc", but I'm puzzled as to why you've been given X,Y in terms of R,Theta.
Original post by ghostwalker
I would have simply said f(x,y)=1/"area of disc", but I'm puzzled as to why you've been given X,Y in terms of R,Theta.
I thought the same yeah, seems strange.
Original post by pineapplechemist
I thought the same yeah, seems strange.
Is that the exact wording of the question?
Original post by ghostwalker
Is that the exact wording of the question?
Yep, exact.
Original post by pineapplechemist
Yep, exact.
OK - I stand by my original post then.
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