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## Homework Statement

I am trying to follow a step in the text book but I don't understand.

[itex]var\left(\frac{1}{N}\sum_{n=0}^{N-1}w[n]\right)\\

=\frac{1}{N^2}\sum_{n=0}^{N-1}var(w[n])[/itex]

where [itex]w[n][/itex] is a Gaussian random variable with mean = 0 and variance = 1

## Homework Equations

[itex]Var(X) = \operatorname{E}\left[X^2 \right] - (\operatorname{E}[X])^2.

[/itex]

## The Attempt at a Solution

The mean is 0 because a summation of Gaussian is Gaussian.

But squaring the whole expression doesn't seem right as there seems to be a trick used to go from line 1 to 2.

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