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Random Variable vs data vs random sample
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I have a problem understanding the difference between random variable and random sample. I have read this thread, but still it is unclear.
According to wiki random variable is a function that from a set of outcomes (events) to measurable values $Omega$ ->$E$ where $E$ could be $mathbbR$. And random sample is a possible outcome.
So I have in a script this sentence which confuses me: let $D=x_1,x_2,x_3...x_n$ be a set of random variables. Now I want to make a sample for myself what $x_1,x_2,...,x_n$ could be.
Let's take the sample of two dices where we want to compute the probability of the sum of the figures of dices we have thrown. So we construct a random variable $X$ which just adds the thrown number of the dices:
$$X:OmegatomathbbN$$
$$X(textdice_1,textdice_2) = textdice_1 + textdice_2 $$
Where dice are uniformly distributed in $ 1,cdots,6 $.
And as far I know, if I throw two dices, I have concrete values which are my random samples.
Now my concrete question is: what could be in this specific example a set of random variables $D=x_1,x_2,x_3...x_n$? And what are then the concrete random samples?
UPDATE:
After reading the comments and replies, I want to underline, that I have a specific question and I would appreciate if someone could answer it explicitly:
In the above example please give me a concrete $D = x_1,x_2,...,x_n$ as a set of random variables. I want to see how a set of random variables $D = x_1,x_2,...,x_n$ (more than 2 random variables) would look like in this example.
probability random-variables
asked Jul 16 at 17:35
Mo Prog
1307
add a comment |Â
up vote
2
down vote
favorite
I have a problem understanding the difference between random variable and random sample. I have read this thread, but still it is unclear.
According to wiki random variable is a function that from a set of outcomes (events) to measurable values $Omega$ ->$E$ where $E$ could be $mathbbR$. And random sample is a possible outcome.
So I have in a script this sentence which confuses me: let $D=x_1,x_2,x_3...x_n$ be a set of random variables. Now I want to make a sample for myself what $x_1,x_2,...,x_n$ could be.
Let's take the sample of two dices where we want to compute the probability of the sum of the figures of dices we have thrown. So we construct a random variable $X$ which just adds the thrown number of the dices:
$$X:OmegatomathbbN$$
$$X(textdice_1,textdice_2) = textdice_1 + textdice_2 $$
Where dice are uniformly distributed in $ 1,cdots,6 $.
And as far I know, if I throw two dices, I have concrete values which are my random samples.
Now my concrete question is: what could be in this specific example a set of random variables $D=x_1,x_2,x_3...x_n$? And what are then the concrete random samples?
UPDATE:
After reading the comments and replies, I want to underline, that I have a specific question and I would appreciate if someone could answer it explicitly:
In the above example please give me a concrete $D = x_1,x_2,...,x_n$ as a set of random variables. I want to see how a set of random variables $D = x_1,x_2,...,x_n$ (more than 2 random variables) would look like in this example.
probability random-variables
asked Jul 16 at 17:35
Mo Prog
1307
It is important to be aware of the fact that there is a reality and a probabilistic model of the reality. The probabilistic model is usually a probability space $(Omega,mathcal A, P)$. On this space we can define random variables $X_1,dots,X_n$ and "taking a random sample" can be interpreted as picking out some outcome $omegainOmega$ (according to rules that are determined by the probability measure $P$) and then having a look at the values $X_1(omega),dots,X_n(omega)$. The reality that corresponds with this picking out can be for instance throwing $n$ times a die.
– drhab
Jul 16 at 19:04
@drhab So in this example a set $D=x_1,x_2...x_n$ would be the outcome of throwing n times a die?
– Mo Prog
Jul 16 at 22:39
In your example I would go for $Omega=(i,j)mid i,jin1,2,3,4,5,6$ and $X_1,X_2$ prescribed respecively by $(i,j)mapsto i$ and $(i,j)mapsto j$. Then you have the random variables $X_1,X_2$ and every outcome $(i,j)$ induces the result of taking a sample: $(X_1(i,j),X_2(i,j))=(i,j)$. It might look redundant because in this simplistic example we get $(X_1,X_2)(omega)=omega$ so the outcome turns up again, but in more complicated situation with lots of data that will be different. Our interest is not in single outcomes but in events like $omegainOmegamid X(omega)in B$.
– drhab
Jul 17 at 8:43
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
I have a problem understanding the difference between random variable and random sample. I have read this thread, but still it is unclear.
According to wiki random variable is a function that from a set of outcomes (events) to measurable values $Omega$ ->$E$ where $E$ could be $mathbbR$. And random sample is a possible outcome.
So I have in a script this sentence which confuses me: let $D=x_1,x_2,x_3...x_n$ be a set of random variables. Now I want to make a sample for myself what $x_1,x_2,...,x_n$ could be.
Let's take the sample of two dices where we want to compute the probability of the sum of the figures of dices we have thrown. So we construct a random variable $X$ which just adds the thrown number of the dices:
$$X:OmegatomathbbN$$
$$X(textdice_1,textdice_2) = textdice_1 + textdice_2 $$
Where dice are uniformly distributed in $ 1,cdots,6 $.
And as far I know, if I throw two dices, I have concrete values which are my random samples.
Now my concrete question is: what could be in this specific example a set of random variables $D=x_1,x_2,x_3...x_n$? And what are then the concrete random samples?
UPDATE:
After reading the comments and replies, I want to underline, that I have a specific question and I would appreciate if someone could answer it explicitly:
In the above example please give me a concrete $D = x_1,x_2,...,x_n$ as a set of random variables. I want to see how a set of random variables $D = x_1,x_2,...,x_n$ (more than 2 random variables) would look like in this example.
probability random-variables
asked Jul 16 at 17:35
Mo Prog
1307
I have a problem understanding the difference between random variable and random sample. I have read this thread, but still it is unclear.
According to wiki random variable is a function that from a set of outcomes (events) to measurable values $Omega$ ->$E$ where $E$ could be $mathbbR$. And random sample is a possible outcome.
So I have in a script this sentence which confuses me: let $D=x_1,x_2,x_3...x_n$ be a set of random variables. Now I want to make a sample for myself what $x_1,x_2,...,x_n$ could be.
Let's take the sample of two dices where we want to compute the probability of the sum of the figures of dices we have thrown. So we construct a random variable $X$ which just adds the thrown number of the dices:
$$X:OmegatomathbbN$$
$$X(textdice_1,textdice_2) = textdice_1 + textdice_2 $$
Where dice are uniformly distributed in $ 1,cdots,6 $.
And as far I know, if I throw two dices, I have concrete values which are my random samples.
Now my concrete question is: what could be in this specific example a set of random variables $D=x_1,x_2,x_3...x_n$? And what are then the concrete random samples?
UPDATE:
After reading the comments and replies, I want to underline, that I have a specific question and I would appreciate if someone could answer it explicitly:
In the above example please give me a concrete $D = x_1,x_2,...,x_n$ as a set of random variables. I want to see how a set of random variables $D = x_1,x_2,...,x_n$ (more than 2 random variables) would look like in this example.
probability random-variables
asked Jul 16 at 17:35
Mo Prog
1307
edited Jul 17 at 9:52
asked Jul 16 at 17:35
Mo Prog
1307
asked Jul 16 at 17:35
Mo Prog
1307
asked Jul 16 at 17:35
Mo Prog
1307
1307
It is important to be aware of the fact that there is a reality and a probabilistic model of the reality. The probabilistic model is usually a probability space $(Omega,mathcal A, P)$. On this space we can define random variables $X_1,dots,X_n$ and "taking a random sample" can be interpreted as picking out some outcome $omegainOmega$ (according to rules that are determined by the probability measure $P$) and then having a look at the values $X_1(omega),dots,X_n(omega)$. The reality that corresponds with this picking out can be for instance throwing $n$ times a die.
– drhab
Jul 16 at 19:04
@drhab So in this example a set $D=x_1,x_2...x_n$ would be the outcome of throwing n times a die?
– Mo Prog
Jul 16 at 22:39
In your example I would go for $Omega=(i,j)mid i,jin1,2,3,4,5,6$ and $X_1,X_2$ prescribed respecively by $(i,j)mapsto i$ and $(i,j)mapsto j$. Then you have the random variables $X_1,X_2$ and every outcome $(i,j)$ induces the result of taking a sample: $(X_1(i,j),X_2(i,j))=(i,j)$. It might look redundant because in this simplistic example we get $(X_1,X_2)(omega)=omega$ so the outcome turns up again, but in more complicated situation with lots of data that will be different. Our interest is not in single outcomes but in events like $omegainOmegamid X(omega)in B$.
– drhab
Jul 17 at 8:43
add a comment |Â
It is important to be aware of the fact that there is a reality and a probabilistic model of the reality. The probabilistic model is usually a probability space $(Omega,mathcal A, P)$. On this space we can define random variables $X_1,dots,X_n$ and "taking a random sample" can be interpreted as picking out some outcome $omegainOmega$ (according to rules that are determined by the probability measure $P$) and then having a look at the values $X_1(omega),dots,X_n(omega)$. The reality that corresponds with this picking out can be for instance throwing $n$ times a die.
– drhab
Jul 16 at 19:04
@drhab So in this example a set $D=x_1,x_2...x_n$ would be the outcome of throwing n times a die?
– Mo Prog
Jul 16 at 22:39
In your example I would go for $Omega=(i,j)mid i,jin1,2,3,4,5,6$ and $X_1,X_2$ prescribed respecively by $(i,j)mapsto i$ and $(i,j)mapsto j$. Then you have the random variables $X_1,X_2$ and every outcome $(i,j)$ induces the result of taking a sample: $(X_1(i,j),X_2(i,j))=(i,j)$. It might look redundant because in this simplistic example we get $(X_1,X_2)(omega)=omega$ so the outcome turns up again, but in more complicated situation with lots of data that will be different. Our interest is not in single outcomes but in events like $omegainOmegamid X(omega)in B$.
– drhab
Jul 17 at 8:43
It is important to be aware of the fact that there is a reality and a probabilistic model of the reality. The probabilistic model is usually a probability space $(Omega,mathcal A, P)$. On this space we can define random variables $X_1,dots,X_n$ and "taking a random sample" can be interpreted as picking out some outcome $omegainOmega$ (according to rules that are determined by the probability measure $P$) and then having a look at the values $X_1(omega),dots,X_n(omega)$. The reality that corresponds with this picking out can be for instance throwing $n$ times a die.
– drhab
Jul 16 at 19:04
It is important to be aware of the fact that there is a reality and a probabilistic model of the reality. The probabilistic model is usually a probability space $(Omega,mathcal A, P)$. On this space we can define random variables $X_1,dots,X_n$ and "taking a random sample" can be interpreted as picking out some outcome $omegainOmega$ (according to rules that are determined by the probability measure $P$) and then having a look at the values $X_1(omega),dots,X_n(omega)$. The reality that corresponds with this picking out can be for instance throwing $n$ times a die.
– drhab
Jul 16 at 19:04
@drhab So in this example a set $D=x_1,x_2...x_n$ would be the outcome of throwing n times a die?
– Mo Prog
Jul 16 at 22:39
@drhab So in this example a set $D=x_1,x_2...x_n$ would be the outcome of throwing n times a die?
– Mo Prog
Jul 16 at 22:39
In your example I would go for $Omega=(i,j)mid i,jin1,2,3,4,5,6$ and $X_1,X_2$ prescribed respecively by $(i,j)mapsto i$ and $(i,j)mapsto j$. Then you have the random variables $X_1,X_2$ and every outcome $(i,j)$ induces the result of taking a sample: $(X_1(i,j),X_2(i,j))=(i,j)$. It might look redundant because in this simplistic example we get $(X_1,X_2)(omega)=omega$ so the outcome turns up again, but in more complicated situation with lots of data that will be different. Our interest is not in single outcomes but in events like $omegainOmegamid X(omega)in B$.
– drhab
Jul 17 at 8:43
In your example I would go for $Omega=(i,j)mid i,jin1,2,3,4,5,6$ and $X_1,X_2$ prescribed respecively by $(i,j)mapsto i$ and $(i,j)mapsto j$. Then you have the random variables $X_1,X_2$ and every outcome $(i,j)$ induces the result of taking a sample: $(X_1(i,j),X_2(i,j))=(i,j)$. It might look redundant because in this simplistic example we get $(X_1,X_2)(omega)=omega$ so the outcome turns up again, but in more complicated situation with lots of data that will be different. Our interest is not in single outcomes but in events like $omegainOmegamid X(omega)in B$.
– drhab
Jul 17 at 8:43
add a comment |Â
1 Answer
1
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up vote
0
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This Three Things are totally different let's talk about them one by one
1.Random Variable: Suppose 'x' is a random variable so it can take any value from a positive number system like 1,2,3,4,5....... and so on
There are two types of random variables:
1.discret: which takes discrete value or we can say exact no like 1,2,3,4...
2.continuous: Which Takes Values like from 1 to 10 so we can say it may be 1.1111 or 3.444 or maybe 9.867545 anything
2.Data: Data Means Collection of lots of variables which has some labels
like data of maturity in different ages
age-group: [1-10] [10-20]
maturity:-- [0.1] [0.2]
So this is Data By which We can Get to the some specific result
3.Random Sample: Part Randomly Taken From Data We can say if we have a large amount of data we can not study on whole data then we take random part of data and them to study on that
answered Jul 16 at 19:42
Parag Jain
86
Can you please now give an example what a set of random variables $x_1,x_2,...x_n$ in my example is?
– Mo Prog
Jul 16 at 22:37
I would call this "the answer of a statistician" (so with strong focus on reality, and less on the probabilistic model that makes it possible to apply mathematics).
– drhab
Jul 17 at 8:51
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
This Three Things are totally different let's talk about them one by one
1.Random Variable: Suppose 'x' is a random variable so it can take any value from a positive number system like 1,2,3,4,5....... and so on
There are two types of random variables:
1.discret: which takes discrete value or we can say exact no like 1,2,3,4...
2.continuous: Which Takes Values like from 1 to 10 so we can say it may be 1.1111 or 3.444 or maybe 9.867545 anything
2.Data: Data Means Collection of lots of variables which has some labels
like data of maturity in different ages
age-group: [1-10] [10-20]
maturity:-- [0.1] [0.2]
So this is Data By which We can Get to the some specific result
3.Random Sample: Part Randomly Taken From Data We can say if we have a large amount of data we can not study on whole data then we take random part of data and them to study on that
answered Jul 16 at 19:42
Parag Jain
86
Can you please now give an example what a set of random variables $x_1,x_2,...x_n$ in my example is?
– Mo Prog
Jul 16 at 22:37
I would call this "the answer of a statistician" (so with strong focus on reality, and less on the probabilistic model that makes it possible to apply mathematics).
– drhab
Jul 17 at 8:51
add a comment |Â
up vote
0
down vote
This Three Things are totally different let's talk about them one by one
1.Random Variable: Suppose 'x' is a random variable so it can take any value from a positive number system like 1,2,3,4,5....... and so on
There are two types of random variables:
1.discret: which takes discrete value or we can say exact no like 1,2,3,4...
2.continuous: Which Takes Values like from 1 to 10 so we can say it may be 1.1111 or 3.444 or maybe 9.867545 anything
2.Data: Data Means Collection of lots of variables which has some labels
like data of maturity in different ages
age-group: [1-10] [10-20]
maturity:-- [0.1] [0.2]
So this is Data By which We can Get to the some specific result
3.Random Sample: Part Randomly Taken From Data We can say if we have a large amount of data we can not study on whole data then we take random part of data and them to study on that
answered Jul 16 at 19:42
Parag Jain
86
Can you please now give an example what a set of random variables $x_1,x_2,...x_n$ in my example is?
– Mo Prog
Jul 16 at 22:37
I would call this "the answer of a statistician" (so with strong focus on reality, and less on the probabilistic model that makes it possible to apply mathematics).
– drhab
Jul 17 at 8:51
add a comment |Â
up vote
0
down vote
up vote
0
down vote
This Three Things are totally different let's talk about them one by one
1.Random Variable: Suppose 'x' is a random variable so it can take any value from a positive number system like 1,2,3,4,5....... and so on
There are two types of random variables:
1.discret: which takes discrete value or we can say exact no like 1,2,3,4...
2.continuous: Which Takes Values like from 1 to 10 so we can say it may be 1.1111 or 3.444 or maybe 9.867545 anything
2.Data: Data Means Collection of lots of variables which has some labels
like data of maturity in different ages
age-group: [1-10] [10-20]
maturity:-- [0.1] [0.2]
So this is Data By which We can Get to the some specific result
3.Random Sample: Part Randomly Taken From Data We can say if we have a large amount of data we can not study on whole data then we take random part of data and them to study on that
answered Jul 16 at 19:42
Parag Jain
86
This Three Things are totally different let's talk about them one by one
1.Random Variable: Suppose 'x' is a random variable so it can take any value from a positive number system like 1,2,3,4,5....... and so on
There are two types of random variables:
1.discret: which takes discrete value or we can say exact no like 1,2,3,4...
2.continuous: Which Takes Values like from 1 to 10 so we can say it may be 1.1111 or 3.444 or maybe 9.867545 anything
2.Data: Data Means Collection of lots of variables which has some labels
like data of maturity in different ages
age-group: [1-10] [10-20]
maturity:-- [0.1] [0.2]
So this is Data By which We can Get to the some specific result
3.Random Sample: Part Randomly Taken From Data We can say if we have a large amount of data we can not study on whole data then we take random part of data and them to study on that
answered Jul 16 at 19:42
Parag Jain
86
answered Jul 16 at 19:42
Parag Jain
86
answered Jul 16 at 19:42
Parag Jain
86
answered Jul 16 at 19:42
Parag Jain
86
86
Can you please now give an example what a set of random variables $x_1,x_2,...x_n$ in my example is?
– Mo Prog
Jul 16 at 22:37
I would call this "the answer of a statistician" (so with strong focus on reality, and less on the probabilistic model that makes it possible to apply mathematics).
– drhab
Jul 17 at 8:51
add a comment |Â
Can you please now give an example what a set of random variables $x_1,x_2,...x_n$ in my example is?
– Mo Prog
Jul 16 at 22:37
I would call this "the answer of a statistician" (so with strong focus on reality, and less on the probabilistic model that makes it possible to apply mathematics).
– drhab
Jul 17 at 8:51
Can you please now give an example what a set of random variables $x_1,x_2,...x_n$ in my example is?
– Mo Prog
Jul 16 at 22:37
Can you please now give an example what a set of random variables $x_1,x_2,...x_n$ in my example is?
– Mo Prog
Jul 16 at 22:37
I would call this "the answer of a statistician" (so with strong focus on reality, and less on the probabilistic model that makes it possible to apply mathematics).
– drhab
Jul 17 at 8:51
I would call this "the answer of a statistician" (so with strong focus on reality, and less on the probabilistic model that makes it possible to apply mathematics).
– drhab
Jul 17 at 8:51
add a comment |Â
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It is important to be aware of the fact that there is a reality and a probabilistic model of the reality. The probabilistic model is usually a probability space $(Omega,mathcal A, P)$. On this space we can define random variables $X_1,dots,X_n$ and "taking a random sample" can be interpreted as picking out some outcome $omegainOmega$ (according to rules that are determined by the probability measure $P$) and then having a look at the values $X_1(omega),dots,X_n(omega)$. The reality that corresponds with this picking out can be for instance throwing $n$ times a die.
– drhab
Jul 16 at 19:04
@drhab So in this example a set $D=x_1,x_2...x_n$ would be the outcome of throwing n times a die?
– Mo Prog
Jul 16 at 22:39
In your example I would go for $Omega=(i,j)mid i,jin1,2,3,4,5,6$ and $X_1,X_2$ prescribed respecively by $(i,j)mapsto i$ and $(i,j)mapsto j$. Then you have the random variables $X_1,X_2$ and every outcome $(i,j)$ induces the result of taking a sample: $(X_1(i,j),X_2(i,j))=(i,j)$. It might look redundant because in this simplistic example we get $(X_1,X_2)(omega)=omega$ so the outcome turns up again, but in more complicated situation with lots of data that will be different. Our interest is not in single outcomes but in events like $omegainOmegamid X(omega)in B$.
– drhab
Jul 17 at 8:43