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Is there a way to create dependence from one or more streams of independent variables.
Clash Royale CLAN TAG#URR8PPP
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My question is..
Given one or more streams/strings/sequences composed of independent and identically distributed variables is there ANY way of combining/merging/viewing the stream/s that would create a bias or statistical dependency.
Say for example we have I.I.D events A, B, C, D, E, F.
Given any finite length of sequence would we be able to simulate a statistical dependence between these events.
I am aware that by definition the events of each single outcome is independent and unbiased - so to clarify my question a little further - what I mean is - is there a way to statistically overcome the independence of outcomes by any combination of possible methods or parallel streams.
Thank you
probability statistics
edited Jul 22 at 3:33
Michael Hardy
204k23186462
asked Jul 22 at 0:21
Mal123456
62
add a comment |Â
up vote
1
down vote
favorite
My question is..
Given one or more streams/strings/sequences composed of independent and identically distributed variables is there ANY way of combining/merging/viewing the stream/s that would create a bias or statistical dependency.
Say for example we have I.I.D events A, B, C, D, E, F.
Given any finite length of sequence would we be able to simulate a statistical dependence between these events.
I am aware that by definition the events of each single outcome is independent and unbiased - so to clarify my question a little further - what I mean is - is there a way to statistically overcome the independence of outcomes by any combination of possible methods or parallel streams.
Thank you
probability statistics
edited Jul 22 at 3:33
Michael Hardy
204k23186462
asked Jul 22 at 0:21
Mal123456
62
1
Not sure if this is what you were thinking about, but if you consider continuous random variables, then for N independent normal Gaussian random variables (i.e., zero mean, unit variance) xi arranged in vector x, the vector y=Ax will have covariance AA'.
– John Polcari
Jul 22 at 0:32
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
My question is..
Given one or more streams/strings/sequences composed of independent and identically distributed variables is there ANY way of combining/merging/viewing the stream/s that would create a bias or statistical dependency.
Say for example we have I.I.D events A, B, C, D, E, F.
Given any finite length of sequence would we be able to simulate a statistical dependence between these events.
I am aware that by definition the events of each single outcome is independent and unbiased - so to clarify my question a little further - what I mean is - is there a way to statistically overcome the independence of outcomes by any combination of possible methods or parallel streams.
Thank you
probability statistics
edited Jul 22 at 3:33
Michael Hardy
204k23186462
asked Jul 22 at 0:21
Mal123456
62
My question is..
Given one or more streams/strings/sequences composed of independent and identically distributed variables is there ANY way of combining/merging/viewing the stream/s that would create a bias or statistical dependency.
Say for example we have I.I.D events A, B, C, D, E, F.
Given any finite length of sequence would we be able to simulate a statistical dependence between these events.
I am aware that by definition the events of each single outcome is independent and unbiased - so to clarify my question a little further - what I mean is - is there a way to statistically overcome the independence of outcomes by any combination of possible methods or parallel streams.
Thank you
probability statistics
edited Jul 22 at 3:33
Michael Hardy
204k23186462
asked Jul 22 at 0:21
Mal123456
62
edited Jul 22 at 3:33
Michael Hardy
204k23186462
edited Jul 22 at 3:33
Michael Hardy
204k23186462
edited Jul 22 at 3:33
Michael Hardy
204k23186462
204k23186462
asked Jul 22 at 0:21
Mal123456
62
asked Jul 22 at 0:21
Mal123456
62
asked Jul 22 at 0:21
Mal123456
62
62
1
Not sure if this is what you were thinking about, but if you consider continuous random variables, then for N independent normal Gaussian random variables (i.e., zero mean, unit variance) xi arranged in vector x, the vector y=Ax will have covariance AA'.
– John Polcari
Jul 22 at 0:32
add a comment |Â
1
Not sure if this is what you were thinking about, but if you consider continuous random variables, then for N independent normal Gaussian random variables (i.e., zero mean, unit variance) xi arranged in vector x, the vector y=Ax will have covariance AA'.
– John Polcari
Jul 22 at 0:32
1
1
Not sure if this is what you were thinking about, but if you consider continuous random variables, then for N independent normal Gaussian random variables (i.e., zero mean, unit variance) xi arranged in vector x, the vector y=Ax will have covariance AA'.
– John Polcari
Jul 22 at 0:32
Not sure if this is what you were thinking about, but if you consider continuous random variables, then for N independent normal Gaussian random variables (i.e., zero mean, unit variance) xi arranged in vector x, the vector y=Ax will have covariance AA'.
– John Polcari
Jul 22 at 0:32
add a comment |Â
1 Answer
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Suppose $X_1,X_2,X_3,ldots$ are independent identically distributed random variables. Consider the sequence $X_1+X_2, ,,, X_2+X_3, ,,, X_3+X_4, ,,, X_4+X_5,,,,ldots.$ Those are not independent.
answered Jul 22 at 3:35
Michael Hardy
204k23186462
add a comment |Â
1 Answer
1
active
oldest
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Suppose $X_1,X_2,X_3,ldots$ are independent identically distributed random variables. Consider the sequence $X_1+X_2, ,,, X_2+X_3, ,,, X_3+X_4, ,,, X_4+X_5,,,,ldots.$ Those are not independent.
answered Jul 22 at 3:35
Michael Hardy
204k23186462
add a comment |Â
up vote
0
down vote
Suppose $X_1,X_2,X_3,ldots$ are independent identically distributed random variables. Consider the sequence $X_1+X_2, ,,, X_2+X_3, ,,, X_3+X_4, ,,, X_4+X_5,,,,ldots.$ Those are not independent.
answered Jul 22 at 3:35
Michael Hardy
204k23186462
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Suppose $X_1,X_2,X_3,ldots$ are independent identically distributed random variables. Consider the sequence $X_1+X_2, ,,, X_2+X_3, ,,, X_3+X_4, ,,, X_4+X_5,,,,ldots.$ Those are not independent.
answered Jul 22 at 3:35
Michael Hardy
204k23186462
Suppose $X_1,X_2,X_3,ldots$ are independent identically distributed random variables. Consider the sequence $X_1+X_2, ,,, X_2+X_3, ,,, X_3+X_4, ,,, X_4+X_5,,,,ldots.$ Those are not independent.
answered Jul 22 at 3:35
Michael Hardy
204k23186462
answered Jul 22 at 3:35
Michael Hardy
204k23186462
answered Jul 22 at 3:35
Michael Hardy
204k23186462
answered Jul 22 at 3:35
Michael Hardy
204k23186462
204k23186462
add a comment |Â
add a comment |Â
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1
Not sure if this is what you were thinking about, but if you consider continuous random variables, then for N independent normal Gaussian random variables (i.e., zero mean, unit variance) xi arranged in vector x, the vector y=Ax will have covariance AA'.
– John Polcari
Jul 22 at 0:32