if (X,Y) is a random vector in R^2,then define f(X,Y) to be its joint density if

P((X,Y)∈A)=∫f(X,Y)(x,y)dxdy, for all reasonable sets A.

show if (X,Y) is

a random vector with density f(X,Y) and f(X,Y)(x,y)=f(x)g(x) for a pair

non-negative functions f and g then X has density f/(∫f(t)dt) and Y has density

g/(∫g(t)dt) and X and Y are independent.(hints: shat means showing P((X∈A)∩

(X∈B))=P(X∈A)P(X∈B)

can someone help me to construct the proof?