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0

$begingroup$

let us assume we divide a piece of membrane into $n$ parts. Every part contributes with a specific electric potential, which is represented by $X_i$ $i=1,...,n$ random variables. So with probability $p_i$ the part $X_i$ is sending an impulse (mostly this impulse should be in the range of $[0,1]$).

All $X_i$ are independent - maybe we can assume a N(0,1) distribution.

The $X_i$ are dependent on the total membrane voltage V(t). I want to show, that the standard deviation of the sum

$sum_i=1^nX_i$
grows proportional to $sqrtn$

but I dont know, how to deal with the dependency on a function.

Shall i look at

$sum_i=1^nV(X_i)$ ?

I dont know how to handle this issue.

probability-theory probability-distributions standard-deviation

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asked Mar 11 at 10:32

Calculator123Calculator123

1

$endgroup$

add a comment | 

0

$begingroup$

let us assume we divide a piece of membrane into $n$ parts. Every part contributes with a specific electric potential, which is represented by $X_i$ $i=1,...,n$ random variables. So with probability $p_i$ the part $X_i$ is sending an impulse (mostly this impulse should be in the range of $[0,1]$).

All $X_i$ are independent - maybe we can assume a N(0,1) distribution.

The $X_i$ are dependent on the total membrane voltage V(t). I want to show, that the standard deviation of the sum

$sum_i=1^nX_i$
grows proportional to $sqrtn$

but I dont know, how to deal with the dependency on a function.

Shall i look at

$sum_i=1^nV(X_i)$ ?

I dont know how to handle this issue.

probability-theory probability-distributions standard-deviation

share|cite|improve this question

asked Mar 11 at 10:32

Calculator123Calculator123

1

$endgroup$

add a comment | 

$begingroup$

let us assume we divide a piece of membrane into $n$ parts. Every part contributes with a specific electric potential, which is represented by $X_i$ $i=1,...,n$ random variables. So with probability $p_i$ the part $X_i$ is sending an impulse (mostly this impulse should be in the range of $[0,1]$).

All $X_i$ are independent - maybe we can assume a N(0,1) distribution.

The $X_i$ are dependent on the total membrane voltage V(t). I want to show, that the standard deviation of the sum

$sum_i=1^nX_i$
grows proportional to $sqrtn$

but I dont know, how to deal with the dependency on a function.

Shall i look at

$sum_i=1^nV(X_i)$ ?

I dont know how to handle this issue.

probability-theory probability-distributions standard-deviation

share|cite|improve this question

asked Mar 11 at 10:32

Calculator123Calculator123

1

$endgroup$

share|cite|improve this question

asked Mar 11 at 10:32

Calculator123Calculator123

1

share|cite|improve this question

asked Mar 11 at 10:32

Calculator123Calculator123

1

asked Mar 11 at 10:32

Calculator123Calculator123

1

asked Mar 11 at 10:32

Calculator123Calculator123

1