Is there any reason not to use the notation $p_{X mid Y = y}(x)$?
Suppose that $X$ and $Y$ are discrete random variables with PMFs $p_X$ and $p_Y$. The conditional probability mass function of $X$ given that $Y = y$ is often denoted $p_{X mid Y}(x mid y)$ (assuming that $p_Y(y) > 0$). However, is there any reason not to use the notation $p_{X mid Y = y}(x)$ instead? I find the latter notation to be much more clear.
Similarly, if $X$ and $Y$ are jointly continuous random variables with PDFs $f_X$ and $f_Y$, the conditional probability density of $X$ given that $Y = y$ is often denoted $f_{X|Y}(x mid y)$ (assuming that $f_Y(y) > 0$). Is there any reason not to use the notation $f_{X mid Y = y}(x)$ instead? It seems more clear, but perhaps I am missing some subtle point.
Are there any textbooks which use the notation $f_{X mid Y=y}(x)$?
probability notation
asked Nov 22 at 6:06
eternalGoldenBraid
707314
add a comment |
Suppose that $X$ and $Y$ are discrete random variables with PMFs $p_X$ and $p_Y$. The conditional probability mass function of $X$ given that $Y = y$ is often denoted $p_{X mid Y}(x mid y)$ (assuming that $p_Y(y) > 0$). However, is there any reason not to use the notation $p_{X mid Y = y}(x)$ instead? I find the latter notation to be much more clear.
Similarly, if $X$ and $Y$ are jointly continuous random variables with PDFs $f_X$ and $f_Y$, the conditional probability density of $X$ given that $Y = y$ is often denoted $f_{X|Y}(x mid y)$ (assuming that $f_Y(y) > 0$). Is there any reason not to use the notation $f_{X mid Y = y}(x)$ instead? It seems more clear, but perhaps I am missing some subtle point.
Are there any textbooks which use the notation $f_{X mid Y=y}(x)$?
probability notation
asked Nov 22 at 6:06
eternalGoldenBraid
707314
It is fine to use the latter notation since the argument is $x$.
– StubbornAtom
Nov 22 at 6:12
Actually I'd almost prefer just dispensing with the '$=y$' bit altogether but definitely like your suggestion (maybe ppl do use it? Have generally seen the more cumbersome version...)
– Mehness
Nov 22 at 6:24
I remember I have seen it (not sure in text/notes), and I even write $f_{X|Y = y}(x mid y)$...
– BGM
Nov 22 at 6:47
1
I use this notation myself.
– Gabriel Romon
Nov 22 at 14:31
add a comment |
Suppose that $X$ and $Y$ are discrete random variables with PMFs $p_X$ and $p_Y$. The conditional probability mass function of $X$ given that $Y = y$ is often denoted $p_{X mid Y}(x mid y)$ (assuming that $p_Y(y) > 0$). However, is there any reason not to use the notation $p_{X mid Y = y}(x)$ instead? I find the latter notation to be much more clear.
Similarly, if $X$ and $Y$ are jointly continuous random variables with PDFs $f_X$ and $f_Y$, the conditional probability density of $X$ given that $Y = y$ is often denoted $f_{X|Y}(x mid y)$ (assuming that $f_Y(y) > 0$). Is there any reason not to use the notation $f_{X mid Y = y}(x)$ instead? It seems more clear, but perhaps I am missing some subtle point.
Are there any textbooks which use the notation $f_{X mid Y=y}(x)$?
probability notation
asked Nov 22 at 6:06
eternalGoldenBraid
707314
Suppose that $X$ and $Y$ are discrete random variables with PMFs $p_X$ and $p_Y$. The conditional probability mass function of $X$ given that $Y = y$ is often denoted $p_{X mid Y}(x mid y)$ (assuming that $p_Y(y) > 0$). However, is there any reason not to use the notation $p_{X mid Y = y}(x)$ instead? I find the latter notation to be much more clear.
Similarly, if $X$ and $Y$ are jointly continuous random variables with PDFs $f_X$ and $f_Y$, the conditional probability density of $X$ given that $Y = y$ is often denoted $f_{X|Y}(x mid y)$ (assuming that $f_Y(y) > 0$). Is there any reason not to use the notation $f_{X mid Y = y}(x)$ instead? It seems more clear, but perhaps I am missing some subtle point.
Are there any textbooks which use the notation $f_{X mid Y=y}(x)$?
probability notation
probability notation
asked Nov 22 at 6:06
eternalGoldenBraid
707314
asked Nov 22 at 6:06
eternalGoldenBraid
707314
edited Nov 22 at 13:29
asked Nov 22 at 6:06
eternalGoldenBraid
707314
asked Nov 22 at 6:06
eternalGoldenBraid
707314
asked Nov 22 at 6:06
eternalGoldenBraid
707314
707314
It is fine to use the latter notation since the argument is $x$.
– StubbornAtom
Nov 22 at 6:12
Actually I'd almost prefer just dispensing with the '$=y$' bit altogether but definitely like your suggestion (maybe ppl do use it? Have generally seen the more cumbersome version...)
– Mehness
Nov 22 at 6:24
I remember I have seen it (not sure in text/notes), and I even write $f_{X|Y = y}(x mid y)$...
– BGM
Nov 22 at 6:47
1
I use this notation myself.
– Gabriel Romon
Nov 22 at 14:31
add a comment |
It is fine to use the latter notation since the argument is $x$.
– StubbornAtom
Nov 22 at 6:12
Actually I'd almost prefer just dispensing with the '$=y$' bit altogether but definitely like your suggestion (maybe ppl do use it? Have generally seen the more cumbersome version...)
– Mehness
Nov 22 at 6:24
I remember I have seen it (not sure in text/notes), and I even write $f_{X|Y = y}(x mid y)$...
– BGM
Nov 22 at 6:47
1
I use this notation myself.
– Gabriel Romon
Nov 22 at 14:31
It is fine to use the latter notation since the argument is $x$.
– StubbornAtom
Nov 22 at 6:12
It is fine to use the latter notation since the argument is $x$.
– StubbornAtom
Nov 22 at 6:12
Actually I'd almost prefer just dispensing with the '$=y$' bit altogether but definitely like your suggestion (maybe ppl do use it? Have generally seen the more cumbersome version...)
– Mehness
Nov 22 at 6:24
Actually I'd almost prefer just dispensing with the '$=y$' bit altogether but definitely like your suggestion (maybe ppl do use it? Have generally seen the more cumbersome version...)
– Mehness
Nov 22 at 6:24
I remember I have seen it (not sure in text/notes), and I even write $f_{X|Y = y}(x mid y)$...
– BGM
Nov 22 at 6:47
I remember I have seen it (not sure in text/notes), and I even write $f_{X|Y = y}(x mid y)$...
– BGM
Nov 22 at 6:47
1
1
I use this notation myself.
– Gabriel Romon
Nov 22 at 14:31
I use this notation myself.
– Gabriel Romon
Nov 22 at 14:31
add a comment |
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It is fine to use the latter notation since the argument is $x$.
– StubbornAtom
Nov 22 at 6:12
Actually I'd almost prefer just dispensing with the '$=y$' bit altogether but definitely like your suggestion (maybe ppl do use it? Have generally seen the more cumbersome version...)
– Mehness
Nov 22 at 6:24
I remember I have seen it (not sure in text/notes), and I even write $f_{X|Y = y}(x mid y)$...
– BGM
Nov 22 at 6:47
1
I use this notation myself.
– Gabriel Romon
Nov 22 at 14:31