Mixing
How to read equation for summing probabilities of each member in a set?
$begingroup$
I’m reading through a chapter in https://www.probabilitycourse.com
There is a section ...
Consider a discrete random variable X with range $Range(X)=R_X$. Note that by definition the PMF is a probability measure, so it satisfies all properties of a probability measure. In particular, we have
$0 leq P_X(x) leq 1$ for all $x$, and
- $Sigma_{ x in R_X}P_X(x)=1$
How do I read the bottom equation? Is it ...
Sum of all the probabilities of X for each x in $R_X$
probability random-variables
asked Feb 1 at 22:05
Chris SnowChris Snow
1738
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add a comment |
$begingroup$
I’m reading through a chapter in https://www.probabilitycourse.com
There is a section ...
Consider a discrete random variable X with range $Range(X)=R_X$. Note that by definition the PMF is a probability measure, so it satisfies all properties of a probability measure. In particular, we have
$0 leq P_X(x) leq 1$ for all $x$, and
- $Sigma_{ x in R_X}P_X(x)=1$
How do I read the bottom equation? Is it ...
Sum of all the probabilities of X for each x in $R_X$
probability random-variables
asked Feb 1 at 22:05
Chris SnowChris Snow
1738
$endgroup$
add a comment |
$begingroup$
I’m reading through a chapter in https://www.probabilitycourse.com
There is a section ...
Consider a discrete random variable X with range $Range(X)=R_X$. Note that by definition the PMF is a probability measure, so it satisfies all properties of a probability measure. In particular, we have
$0 leq P_X(x) leq 1$ for all $x$, and
- $Sigma_{ x in R_X}P_X(x)=1$
How do I read the bottom equation? Is it ...
Sum of all the probabilities of X for each x in $R_X$
probability random-variables
asked Feb 1 at 22:05
Chris SnowChris Snow
1738
$endgroup$
I’m reading through a chapter in https://www.probabilitycourse.com
There is a section ...
Consider a discrete random variable X with range $Range(X)=R_X$. Note that by definition the PMF is a probability measure, so it satisfies all properties of a probability measure. In particular, we have
$0 leq P_X(x) leq 1$ for all $x$, and
- $Sigma_{ x in R_X}P_X(x)=1$
How do I read the bottom equation? Is it ...
Sum of all the probabilities of X for each x in $R_X$
probability random-variables
probability random-variables
asked Feb 1 at 22:05
Chris SnowChris Snow
1738
asked Feb 1 at 22:05
Chris SnowChris Snow
1738
asked Feb 1 at 22:05
Chris SnowChris Snow
1738
asked Feb 1 at 22:05
Chris SnowChris Snow
1738
asked Feb 1 at 22:05
Chris SnowChris Snow
1738
1738
add a comment |
add a comment |
1 Answer
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You sum over all x's which are in $R_x=Range(X)={x in mathbb{R} | x=X(omega) }$ for some $omega$ in the sample sample}.
So yes, you read that correctly.
answered Feb 1 at 22:11
AlexandrosAlexandros
1,0601413
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add a comment |
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1 Answer
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1 Answer
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$begingroup$
You sum over all x's which are in $R_x=Range(X)={x in mathbb{R} | x=X(omega) }$ for some $omega$ in the sample sample}.
So yes, you read that correctly.
answered Feb 1 at 22:11
AlexandrosAlexandros
1,0601413
$endgroup$
add a comment |
$begingroup$
You sum over all x's which are in $R_x=Range(X)={x in mathbb{R} | x=X(omega) }$ for some $omega$ in the sample sample}.
So yes, you read that correctly.
answered Feb 1 at 22:11
AlexandrosAlexandros
1,0601413
$endgroup$
add a comment |
$begingroup$
You sum over all x's which are in $R_x=Range(X)={x in mathbb{R} | x=X(omega) }$ for some $omega$ in the sample sample}.
So yes, you read that correctly.
answered Feb 1 at 22:11
AlexandrosAlexandros
1,0601413
$endgroup$
You sum over all x's which are in $R_x=Range(X)={x in mathbb{R} | x=X(omega) }$ for some $omega$ in the sample sample}.
So yes, you read that correctly.
answered Feb 1 at 22:11
AlexandrosAlexandros
1,0601413
answered Feb 1 at 22:11
AlexandrosAlexandros
1,0601413
answered Feb 1 at 22:11
AlexandrosAlexandros
1,0601413
answered Feb 1 at 22:11
AlexandrosAlexandros
1,0601413
1,0601413
add a comment |
add a comment |
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