- #1
SeriousNoob
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Homework Statement
I am trying to follow a step in the textbook 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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