I'm assuming V(Xn) is variance. Is there not a way to write variance in terms of Expectation? This is beyond my scope, but that's one thing I'm thinking about.
X1, X2,.......Xn is a sequence of random variables. Show that Xn converges to b in quadratic mean if and only if
The limit (n approaching infinity) of E(Xn) = b and
The limit (n approaching infinity) of V(Xn) = 0.
We know that Xn converges to X in quadratic mean if E(Xn - X)^2 -> 0 as n approaches infinity and Xn converges to c in quadratic mean if E(Xn - c)^2 -> 0 as n approaches infinity.
What's throwing me is the presence of V in terms of solving the problem. Any assistance would be greatly appreciated. Thanks.
I'm assuming V(Xn) is variance. Is there not a way to write variance in terms of Expectation? This is beyond my scope, but that's one thing I'm thinking about.
"I have discovered a truly remarkable proof of this theorem which this margin is too narrow to contain." Pierre de Fermat
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