Why do we define random variable models of probability distributions in the following manner. [closed]

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I am wondering why are random variable models of probability distributions defined like this:

Let X be the random variable that represents the NEXT measurement?

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asked Aug 1 at 20:55

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closed as unclear what you're asking by Did, Xander Henderson, amWhy, Lord Shark the Unknown, max_zorn Aug 2 at 5:58

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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up vote
-2
down vote

favorite

I am wondering why are random variable models of probability distributions defined like this:

Let X be the random variable that represents the NEXT measurement?

statistics

share|cite|improve this question

asked Aug 1 at 20:55

Hello

1

closed as unclear what you're asking by Did, Xander Henderson, amWhy, Lord Shark the Unknown, max_zorn Aug 2 at 5:58

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

add a comment | 

up vote
-2
down vote

favorite

up vote
-2
down vote

favorite

I am wondering why are random variable models of probability distributions defined like this:

Let X be the random variable that represents the NEXT measurement?

statistics

share|cite|improve this question

asked Aug 1 at 20:55

Hello

1

I am wondering why are random variable models of probability distributions defined like this:

Let X be the random variable that represents the NEXT measurement?

statistics

share|cite|improve this question

asked Aug 1 at 20:55

Hello

1

share|cite|improve this question

share|cite|improve this question

asked Aug 1 at 20:55

Hello

1

asked Aug 1 at 20:55

Hello

1

asked Aug 1 at 20:55

Hello

1

1

closed as unclear what you're asking by Did, Xander Henderson, amWhy, Lord Shark the Unknown, max_zorn Aug 2 at 5:58

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

closed as unclear what you're asking by Did, Xander Henderson, amWhy, Lord Shark the Unknown, max_zorn Aug 2 at 5:58

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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It's just a formulation of your special case. Maybe it means exactly what's written there. Can't be answered without context tho.

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answered Aug 1 at 21:23

til

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  Thanks for your response.
  – Hello
  Aug 1 at 22:06
  

  
  
  
  

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Some authors use the word 'next' in connection with random variables to highlight the point that probability statements ought to be made only on experiments that have not been carried out yet, in which case there is some uncertainty about the result of the experiment; they don't apply to the observed result of an already-completed experiment, where all the uncertainty is gone.

Example: Roll a die once. You can ask what is the probability that the next roll equals four. The answer is $P(X=4)=frac16$, where $X$ denotes the next roll. But if you carry out the experiment and observe a three, you can't substitute the observed value $3$ in place of $X$; there's no point in asking what is $P(3=4)$, and the answer is not $frac16$.

It's not essential to use the word 'next' when talking about random variables, or probability in general, as long as it's understood that we are asking questions in the context of an experiment where uncertainty or chance plays a role. In that sense, the word 'next' is a way to insert a probability distribution into an experimental procedure; it's often shorthand for verbiage like 'pick a subject uniformly at random from a larger population'.

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answered Aug 1 at 22:23

grand_chat

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2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
0
down vote

It's just a formulation of your special case. Maybe it means exactly what's written there. Can't be answered without context tho.

share|cite|improve this answer

answered Aug 1 at 21:23

til

694

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for your response.
  – Hello
  Aug 1 at 22:06
  

  
  
  
  

add a comment | 

up vote
0
down vote

It's just a formulation of your special case. Maybe it means exactly what's written there. Can't be answered without context tho.

share|cite|improve this answer

answered Aug 1 at 21:23

til

694

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for your response.
  – Hello
  Aug 1 at 22:06
  

  
  
  
  

add a comment | 

up vote
0
down vote

up vote
0
down vote

It's just a formulation of your special case. Maybe it means exactly what's written there. Can't be answered without context tho.

share|cite|improve this answer

answered Aug 1 at 21:23

til

694

It's just a formulation of your special case. Maybe it means exactly what's written there. Can't be answered without context tho.

share|cite|improve this answer

answered Aug 1 at 21:23

til

694

share|cite|improve this answer

share|cite|improve this answer

answered Aug 1 at 21:23

til

694

answered Aug 1 at 21:23

til

694

answered Aug 1 at 21:23

til

694

694

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for your response.
  – Hello
  Aug 1 at 22:06
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for your response.
  – Hello
  Aug 1 at 22:06
  

  
  
  
  

Thanks for your response.
– Hello
Aug 1 at 22:06

Thanks for your response.
– Hello
Aug 1 at 22:06

add a comment | 

up vote
0
down vote

Some authors use the word 'next' in connection with random variables to highlight the point that probability statements ought to be made only on experiments that have not been carried out yet, in which case there is some uncertainty about the result of the experiment; they don't apply to the observed result of an already-completed experiment, where all the uncertainty is gone.

Example: Roll a die once. You can ask what is the probability that the next roll equals four. The answer is $P(X=4)=frac16$, where $X$ denotes the next roll. But if you carry out the experiment and observe a three, you can't substitute the observed value $3$ in place of $X$; there's no point in asking what is $P(3=4)$, and the answer is not $frac16$.

It's not essential to use the word 'next' when talking about random variables, or probability in general, as long as it's understood that we are asking questions in the context of an experiment where uncertainty or chance plays a role. In that sense, the word 'next' is a way to insert a probability distribution into an experimental procedure; it's often shorthand for verbiage like 'pick a subject uniformly at random from a larger population'.

share|cite|improve this answer

answered Aug 1 at 22:23

grand_chat

17.8k11120

add a comment | 

up vote
0
down vote

Some authors use the word 'next' in connection with random variables to highlight the point that probability statements ought to be made only on experiments that have not been carried out yet, in which case there is some uncertainty about the result of the experiment; they don't apply to the observed result of an already-completed experiment, where all the uncertainty is gone.

Example: Roll a die once. You can ask what is the probability that the next roll equals four. The answer is $P(X=4)=frac16$, where $X$ denotes the next roll. But if you carry out the experiment and observe a three, you can't substitute the observed value $3$ in place of $X$; there's no point in asking what is $P(3=4)$, and the answer is not $frac16$.

It's not essential to use the word 'next' when talking about random variables, or probability in general, as long as it's understood that we are asking questions in the context of an experiment where uncertainty or chance plays a role. In that sense, the word 'next' is a way to insert a probability distribution into an experimental procedure; it's often shorthand for verbiage like 'pick a subject uniformly at random from a larger population'.

share|cite|improve this answer

answered Aug 1 at 22:23

grand_chat

17.8k11120

add a comment | 

up vote
0
down vote

up vote
0
down vote

Some authors use the word 'next' in connection with random variables to highlight the point that probability statements ought to be made only on experiments that have not been carried out yet, in which case there is some uncertainty about the result of the experiment; they don't apply to the observed result of an already-completed experiment, where all the uncertainty is gone.

Example: Roll a die once. You can ask what is the probability that the next roll equals four. The answer is $P(X=4)=frac16$, where $X$ denotes the next roll. But if you carry out the experiment and observe a three, you can't substitute the observed value $3$ in place of $X$; there's no point in asking what is $P(3=4)$, and the answer is not $frac16$.

It's not essential to use the word 'next' when talking about random variables, or probability in general, as long as it's understood that we are asking questions in the context of an experiment where uncertainty or chance plays a role. In that sense, the word 'next' is a way to insert a probability distribution into an experimental procedure; it's often shorthand for verbiage like 'pick a subject uniformly at random from a larger population'.

share|cite|improve this answer

answered Aug 1 at 22:23

grand_chat

17.8k11120

Some authors use the word 'next' in connection with random variables to highlight the point that probability statements ought to be made only on experiments that have not been carried out yet, in which case there is some uncertainty about the result of the experiment; they don't apply to the observed result of an already-completed experiment, where all the uncertainty is gone.

Example: Roll a die once. You can ask what is the probability that the next roll equals four. The answer is $P(X=4)=frac16$, where $X$ denotes the next roll. But if you carry out the experiment and observe a three, you can't substitute the observed value $3$ in place of $X$; there's no point in asking what is $P(3=4)$, and the answer is not $frac16$.

It's not essential to use the word 'next' when talking about random variables, or probability in general, as long as it's understood that we are asking questions in the context of an experiment where uncertainty or chance plays a role. In that sense, the word 'next' is a way to insert a probability distribution into an experimental procedure; it's often shorthand for verbiage like 'pick a subject uniformly at random from a larger population'.

share|cite|improve this answer

answered Aug 1 at 22:23

grand_chat

17.8k11120

share|cite|improve this answer

share|cite|improve this answer

answered Aug 1 at 22:23

grand_chat

17.8k11120

answered Aug 1 at 22:23

grand_chat

17.8k11120

answered Aug 1 at 22:23

grand_chat

17.8k11120

17.8k11120

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