- #1

Pushoam

- 962

- 52

## Homework Statement

## Homework Equations

## The Attempt at a Solution

The probability that ##X_1 ## is between ## X_1 ## and ## X_1 + dX_1 ## and ##X_2 ## is between ## X_2 ## and ## X_2 + dX_2 ## and so on till the nth variable is

dP(##X_1,

X_2, ..., X_n) = p ( X_1) p( x_2) p(X_3)...p(X_n) dX_1 dX_2 ...dX_n

\\ dP(Y) = p(Y) dY

\\<Y>= \int Yp(Y) dY

\\ assuming dP(y) =

dP(X_1,

X_2, ..., X_n)

\\= \int ( X_1 +X_2 + ... + X_n) p ( X_1) p( x_2) p(X_3)...p(X_n) dX_1 dX_2 ...dX_n

\\ = \int X_1 p ( X_1)dX_1+ \int X_2 p ( X_2)dX_2+ ...+\int X_n p ( X_n)dX_n

\\= <X_1> + <X_2>+...+<X_n>

\\= n <X>##

Is the assumption o.k?