For random variables (X,Y) = (R*cos(V),R*sin(V))(adsbygoogle = window.adsbygoogle || []).push({});

I have R_PDF(r) = 2*r/K^2

and V_PDF(v) = 1/(2*pi)

where (0 < r < K) and (0 < v < 2*pi)

Is XY_PDF(x,y) the joint density of X and Y that I get by using the PDF method with Jacobians from the distribution R_PDF(r)*V_PDF(v)?

So without having R_PDF(r) and V_PDF(v), just knowing that X^2+Y^2=R^2 - if I want to get XY_PDF(x,y) I would first need to find two independent variables describing both X and Y, then those independent variables marginal distributions in order to create the independent variables joint distribution and then I can calculate XY_PDF(x,y)?

Because only independent marginal distributions can be multiplied to form a joint density?

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# I Joint distributions

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