Variance of the sum of random independent variables

[dipole]

Homework Statement

let x_{i} be a random variable, and let y_{j} = \sum x_{i}.

The variance of the random distribution of the x_{i}'s is known, and each y is the sum of an equal amount of x_{i}'s, say N of them.

How do I compute the variance of y in terms of \sigma^2_{x} and N?

Homework Equations

\sigma^2_{y} = \sum\frac{(y - \mu_{y})^2}{M}

 

[dipole]

Also forgot to mention that I already know that \mu_{y} = N\mu_{x}.

 

[Ray Vickson]

Homework Statement

let x_{i} be a random variable, and let y_{j} = \sum x_{i}.

The variance of the random distribution of the x_{i}'s is known, and each y is the sum of an equal amount of x_{i}'s, say N of them.

How do I compute the variance of y in terms of \sigma^2_{x} and N?

Homework Equations

\sigma^2_{y} = \sum\frac{(y - \mu_{y})^2}{M}

I don't understand your formula for \sigma^2_{y}, which would be false for every probability distribution I can think of. (It assumes Y is a uniformly-distributed random variable taking M distinct values.)

Start with the simple case N=2: Y = X_1 + X_2, where X_1,\; X_2 are independent. Once you have done that case, the general case follows almost immediately.

RGV