Suppose two random variable $X$ and $Y$. Does if $E(X)>E(Y)$, then $\text{Var}(X) > \text{Var}(Y)$? I think not, but I am not sure how to disprove it. I know that $\text{Var}(X) = E(X^2)- E(X)^2 > \text{Var}(Y)=E(Y^2) -E(Y)^2 $ implies $E(X^2) - E(Y^2) > E(X)^2 - E(Y)^2 > 0$, but I am not sure if I can use it to disprove the hypothesis. Can you give me a hint?
2026-04-04 04:18:16.1775276296
Does if $E(X)>E(Y)$, then $\text{Var}(X) > \text{Var}(Y)$?
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Take $X=Y+1$. Then $EX>EY$ but $var (X)=var(Y)$.