Expected pairwise square euclidean distance between points
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How can I show that the expected pairwise square euclidean distance between points in $X$ is $Θ(d)$?
Where $X$ is a $(x_1,...x_n)$ of points generated uniformly at random in the unit, d is d-dimensional cube , $x=(x(1),...x(d))$ the generic point has its -th component $x(i)$ chosen uniformly at random in$ [0,1] $independently of other components and points.
$Theta(d)$ represent the largest possible distance is d.
I try to reconduct this problem to Bertrand Paradox but i dont think is right. Maybe I that show that $E(||x−y||2)=Θ(d)$ , because is a hint but i dont know how.
i m following this path: https://stats.stackexchange.com/questions/22488/probability-that-uniformly-random-points-in-a-rectangle-have-euclidean-distance
but is different to my point.
Thanks.
probability probability-theory variance expected-value
asked 57 mins ago
Antonio Luciano
11
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Antonio Luciano is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
0
down vote
favorite
How can I show that the expected pairwise square euclidean distance between points in $X$ is $Θ(d)$?
Where $X$ is a $(x_1,...x_n)$ of points generated uniformly at random in the unit, d is d-dimensional cube , $x=(x(1),...x(d))$ the generic point has its -th component $x(i)$ chosen uniformly at random in$ [0,1] $independently of other components and points.
$Theta(d)$ represent the largest possible distance is d.
I try to reconduct this problem to Bertrand Paradox but i dont think is right. Maybe I that show that $E(||x−y||2)=Θ(d)$ , because is a hint but i dont know how.
i m following this path: https://stats.stackexchange.com/questions/22488/probability-that-uniformly-random-points-in-a-rectangle-have-euclidean-distance
but is different to my point.
Thanks.
probability probability-theory variance expected-value
asked 57 mins ago
Antonio Luciano
11
New contributor
Antonio Luciano is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
54 mins ago
@JoséCarlosSantos Hi Josè , i edit the question adding a math formatting, thanks
– Antonio Luciano
50 mins ago
Your question begins with the words “0 down vote favorite”. Why is that?
– José Carlos Santos
49 mins ago
just a misprint of paste. thanks i don't see @JoséCarlosSantos
– Antonio Luciano
42 mins ago
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
How can I show that the expected pairwise square euclidean distance between points in $X$ is $Θ(d)$?
Where $X$ is a $(x_1,...x_n)$ of points generated uniformly at random in the unit, d is d-dimensional cube , $x=(x(1),...x(d))$ the generic point has its -th component $x(i)$ chosen uniformly at random in$ [0,1] $independently of other components and points.
$Theta(d)$ represent the largest possible distance is d.
I try to reconduct this problem to Bertrand Paradox but i dont think is right. Maybe I that show that $E(||x−y||2)=Θ(d)$ , because is a hint but i dont know how.
i m following this path: https://stats.stackexchange.com/questions/22488/probability-that-uniformly-random-points-in-a-rectangle-have-euclidean-distance
but is different to my point.
Thanks.
probability probability-theory variance expected-value
asked 57 mins ago
Antonio Luciano
11
New contributor
Antonio Luciano is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
How can I show that the expected pairwise square euclidean distance between points in $X$ is $Θ(d)$?
Where $X$ is a $(x_1,...x_n)$ of points generated uniformly at random in the unit, d is d-dimensional cube , $x=(x(1),...x(d))$ the generic point has its -th component $x(i)$ chosen uniformly at random in$ [0,1] $independently of other components and points.
$Theta(d)$ represent the largest possible distance is d.
I try to reconduct this problem to Bertrand Paradox but i dont think is right. Maybe I that show that $E(||x−y||2)=Θ(d)$ , because is a hint but i dont know how.
i m following this path: https://stats.stackexchange.com/questions/22488/probability-that-uniformly-random-points-in-a-rectangle-have-euclidean-distance
but is different to my point.
Thanks.
probability probability-theory variance expected-value
probability probability-theory variance expected-value
asked 57 mins ago
Antonio Luciano
11
New contributor
Antonio Luciano is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 57 mins ago
Antonio Luciano
11
New contributor
Antonio Luciano is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 43 mins ago
asked 57 mins ago
Antonio Luciano
11
New contributor
Antonio Luciano is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 57 mins ago
Antonio Luciano
11
asked 57 mins ago
Antonio Luciano
11
11
New contributor
Antonio Luciano is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Antonio Luciano is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Antonio Luciano is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
54 mins ago
@JoséCarlosSantos Hi Josè , i edit the question adding a math formatting, thanks
– Antonio Luciano
50 mins ago
Your question begins with the words “0 down vote favorite”. Why is that?
– José Carlos Santos
49 mins ago
just a misprint of paste. thanks i don't see @JoséCarlosSantos
– Antonio Luciano
42 mins ago
add a comment |
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
54 mins ago
@JoséCarlosSantos Hi Josè , i edit the question adding a math formatting, thanks
– Antonio Luciano
50 mins ago
Your question begins with the words “0 down vote favorite”. Why is that?
– José Carlos Santos
49 mins ago
just a misprint of paste. thanks i don't see @JoséCarlosSantos
– Antonio Luciano
42 mins ago
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
54 mins ago
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
54 mins ago
@JoséCarlosSantos Hi Josè , i edit the question adding a math formatting, thanks
– Antonio Luciano
50 mins ago
@JoséCarlosSantos Hi Josè , i edit the question adding a math formatting, thanks
– Antonio Luciano
50 mins ago
Your question begins with the words “0 down vote favorite”. Why is that?
– José Carlos Santos
49 mins ago
Your question begins with the words “0 down vote favorite”. Why is that?
– José Carlos Santos
49 mins ago
just a misprint of paste. thanks i don't see @JoséCarlosSantos
– Antonio Luciano
42 mins ago
just a misprint of paste. thanks i don't see @JoséCarlosSantos
– Antonio Luciano
42 mins ago
add a comment |
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Antonio Luciano is a new contributor. Be nice, and check out our Code of Conduct.
Antonio Luciano is a new contributor. Be nice, and check out our Code of Conduct.
Antonio Luciano is a new contributor. Be nice, and check out our Code of Conduct.
Antonio Luciano is a new contributor. Be nice, and check out our Code of Conduct.
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Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
54 mins ago
@JoséCarlosSantos Hi Josè , i edit the question adding a math formatting, thanks
– Antonio Luciano
50 mins ago
Your question begins with the words “0 down vote favorite”. Why is that?
– José Carlos Santos
49 mins ago
just a misprint of paste. thanks i don't see @JoséCarlosSantos
– Antonio Luciano
42 mins ago