Let X and Y be two random variables so that Var(X) >= Var(Y). Is is true that for any real value r>0, Pr (|X| > r) > Pr (|Y| > r)? If yes, give a proof. If no, give a counterexample (i.e., a combination of X, Y, and r that the statement fails).
Added by Joan H.
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This means that X has a wider spread of values than Y, or in other words, X is more variable than Y. Now, let's consider the statement Pr (|X| > r) > Pr (|Y| > r). This means that the probability of X being farther away from 0 than r is higher than the Show more…
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