Monotonicity property of expectation
Multi tool use
$begingroup$
Let $X$ and $Y$ be random variables such that whenever $Xle Y$ we have $f(X)ge f(Y)$, where $f$ is some function on the domain of the random variables (i don't think you'd need any properties of $f$ for this...)
Then, if it holds that $E[X]le E[Y]$, is it true that $E[f(X)]ge E[f(Y)]$. Intuitively this seems like it should be true, but I can't formalize it. If the statement is false as it is, are there conditions under which it would hold?
probability expected-value
asked Dec 1 '18 at 23:41
user114743user114743
1026
$endgroup$
add a comment |
$begingroup$
Let $X$ and $Y$ be random variables such that whenever $Xle Y$ we have $f(X)ge f(Y)$, where $f$ is some function on the domain of the random variables (i don't think you'd need any properties of $f$ for this...)
Then, if it holds that $E[X]le E[Y]$, is it true that $E[f(X)]ge E[f(Y)]$. Intuitively this seems like it should be true, but I can't formalize it. If the statement is false as it is, are there conditions under which it would hold?
probability expected-value
asked Dec 1 '18 at 23:41
user114743user114743
1026
$endgroup$
add a comment |
$begingroup$
Let $X$ and $Y$ be random variables such that whenever $Xle Y$ we have $f(X)ge f(Y)$, where $f$ is some function on the domain of the random variables (i don't think you'd need any properties of $f$ for this...)
Then, if it holds that $E[X]le E[Y]$, is it true that $E[f(X)]ge E[f(Y)]$. Intuitively this seems like it should be true, but I can't formalize it. If the statement is false as it is, are there conditions under which it would hold?
probability expected-value
asked Dec 1 '18 at 23:41
user114743user114743
1026
$endgroup$
Let $X$ and $Y$ be random variables such that whenever $Xle Y$ we have $f(X)ge f(Y)$, where $f$ is some function on the domain of the random variables (i don't think you'd need any properties of $f$ for this...)
Then, if it holds that $E[X]le E[Y]$, is it true that $E[f(X)]ge E[f(Y)]$. Intuitively this seems like it should be true, but I can't formalize it. If the statement is false as it is, are there conditions under which it would hold?
probability expected-value
probability expected-value
asked Dec 1 '18 at 23:41
user114743user114743
1026
asked Dec 1 '18 at 23:41
user114743user114743
1026
asked Dec 1 '18 at 23:41
user114743user114743
1026
asked Dec 1 '18 at 23:41
user114743user114743
1026
asked Dec 1 '18 at 23:41
user114743user114743
1026
1026
add a comment |
add a comment |
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