Mixing
Different notation $dP(x)$ and $P(dx)$
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Quick question that has been bugging me for a while: I have come across both the notation $dP(x)$ as well as $P(dx)$ when looking at the $mathbb E[X]$ where $X$ is a continuous real random variable. Am I missing an important concept as to why both are used, rather than just one? Or are these notations simply equivalent?
probability probability-theory measure-theory random-variables
asked Jan 29 at 17:48
SABOYSABOY
592311
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add a comment |
$begingroup$
Quick question that has been bugging me for a while: I have come across both the notation $dP(x)$ as well as $P(dx)$ when looking at the $mathbb E[X]$ where $X$ is a continuous real random variable. Am I missing an important concept as to why both are used, rather than just one? Or are these notations simply equivalent?
probability probability-theory measure-theory random-variables
asked Jan 29 at 17:48
SABOYSABOY
592311
$endgroup$
$begingroup$
Neither of them means anything in their own except that the integral is with respect to the measure $P.$ In fact, you can drop the "$dx$" symbols everywhere and simply write $mathbf{E}(X) = intlimits_Omega X dP.$
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– Will M.
Jan 29 at 20:27
$begingroup$
They come handy when you have a function of two variables, say $x in Omega$ and $t in mathrm{T}$ and the measure $P$ is on $Omega.$ But even then the fact that $P$ is defined on $Omega$ should suffice...
$endgroup$
– Will M.
Jan 29 at 20:28
add a comment |
$begingroup$
Quick question that has been bugging me for a while: I have come across both the notation $dP(x)$ as well as $P(dx)$ when looking at the $mathbb E[X]$ where $X$ is a continuous real random variable. Am I missing an important concept as to why both are used, rather than just one? Or are these notations simply equivalent?
probability probability-theory measure-theory random-variables
asked Jan 29 at 17:48
SABOYSABOY
592311
$endgroup$
Quick question that has been bugging me for a while: I have come across both the notation $dP(x)$ as well as $P(dx)$ when looking at the $mathbb E[X]$ where $X$ is a continuous real random variable. Am I missing an important concept as to why both are used, rather than just one? Or are these notations simply equivalent?
probability probability-theory measure-theory random-variables
probability probability-theory measure-theory random-variables
asked Jan 29 at 17:48
SABOYSABOY
592311
asked Jan 29 at 17:48
SABOYSABOY
592311
asked Jan 29 at 17:48
SABOYSABOY
592311
asked Jan 29 at 17:48
SABOYSABOY
592311
asked Jan 29 at 17:48
SABOYSABOY
592311
592311
$begingroup$
Neither of them means anything in their own except that the integral is with respect to the measure $P.$ In fact, you can drop the "$dx$" symbols everywhere and simply write $mathbf{E}(X) = intlimits_Omega X dP.$
$endgroup$
– Will M.
Jan 29 at 20:27
$begingroup$
They come handy when you have a function of two variables, say $x in Omega$ and $t in mathrm{T}$ and the measure $P$ is on $Omega.$ But even then the fact that $P$ is defined on $Omega$ should suffice...
$endgroup$
– Will M.
Jan 29 at 20:28
add a comment |
$begingroup$
Neither of them means anything in their own except that the integral is with respect to the measure $P.$ In fact, you can drop the "$dx$" symbols everywhere and simply write $mathbf{E}(X) = intlimits_Omega X dP.$
$endgroup$
– Will M.
Jan 29 at 20:27
$begingroup$
They come handy when you have a function of two variables, say $x in Omega$ and $t in mathrm{T}$ and the measure $P$ is on $Omega.$ But even then the fact that $P$ is defined on $Omega$ should suffice...
$endgroup$
– Will M.
Jan 29 at 20:28
$begingroup$
Neither of them means anything in their own except that the integral is with respect to the measure $P.$ In fact, you can drop the "$dx$" symbols everywhere and simply write $mathbf{E}(X) = intlimits_Omega X dP.$
$endgroup$
– Will M.
Jan 29 at 20:27
$begingroup$
Neither of them means anything in their own except that the integral is with respect to the measure $P.$ In fact, you can drop the "$dx$" symbols everywhere and simply write $mathbf{E}(X) = intlimits_Omega X dP.$
$endgroup$
– Will M.
Jan 29 at 20:27
$begingroup$
They come handy when you have a function of two variables, say $x in Omega$ and $t in mathrm{T}$ and the measure $P$ is on $Omega.$ But even then the fact that $P$ is defined on $Omega$ should suffice...
$endgroup$
– Will M.
Jan 29 at 20:28
$begingroup$
They come handy when you have a function of two variables, say $x in Omega$ and $t in mathrm{T}$ and the measure $P$ is on $Omega.$ But even then the fact that $P$ is defined on $Omega$ should suffice...
$endgroup$
– Will M.
Jan 29 at 20:28
add a comment |
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$begingroup$
Neither of them means anything in their own except that the integral is with respect to the measure $P.$ In fact, you can drop the "$dx$" symbols everywhere and simply write $mathbf{E}(X) = intlimits_Omega X dP.$
$endgroup$
– Will M.
Jan 29 at 20:27
$begingroup$
They come handy when you have a function of two variables, say $x in Omega$ and $t in mathrm{T}$ and the measure $P$ is on $Omega.$ But even then the fact that $P$ is defined on $Omega$ should suffice...
$endgroup$
– Will M.
Jan 29 at 20:28