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## Main Question or Discussion Point

I have two sets of deterministic numbers, collected in the two vectors: x=[x(1),...,x(n)] and y=[y(1),...,y(n)]. My (determinstic) theory says that x(i)=y(i) for all i=1,...,n. But instead, I want to assume that the numbers x and y are stochastic. If we let f(.) be a pdf, does this mean that I can test a stochastic version of my theory by setting up a hypothesis test H0: f(x)=f(y) vs. H1: Not H0? That is, is it true that x=y <=> f(x)=f(y) if f is a pdf?