rv-identically-distributed(p;n.f(n);i.X(i))
== n, m:.
== E(f(n);X(n)) = E(f(m);X(m))
== & E(f(n);(x.x * x) o X(n)) = E(f(m);(x.x * x) o X(m))
== & E(f(n);(x.(x * x) * x) o X(n)) = E(f(m);(x.(x * x) * x) o X(m))
== & E(f(n);(x.(x * x) * x * x) o X(n)) = E(f(m);(x.(x * x) * x * x) o X(m)) 

latex

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clarification:

rv-identically-distributed(p;n.f(n);i.X(i))
== n:, m:.
== expectation(p;f(n);X(n)) = expectation(p;f(m);X(m))  
== & expectation(p;f(n);(x.x * x) o X(n)) = expectation(p;f(m);(x.x * x) o X(m))  
== & expectation(p;f(n);(x.(x * x) * x) o X(n)) = expectation(p;f(m);(x.(x * x) * x) o X(m))  
== & expectation(p;f(n);(x.(x * x) * x * x) o X(n))
== & =
== & expectation(p;f(m);(x.(x * x) * x * x) o X(m))
== &   

latex

Definitions	x:A. B(x), , P & Q, s = t, , E(n;F), (x.F(x)) o X, r * s
FDL editor aliases	rv-identically-distributed