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All $x_i$ are identically distributed: discretely uniformly distributed, with the only values being $\{-\sqrt{\frac12}, \sqrt{\frac12}\}$ on both the real and imaginary part.
The $w_i$ are also identically distributed, as per the problem statement.
Therefore, the variance (this being zero-mean) is simply $\sqrt{\frac12}^2=\frac12$ in each of the real and ...
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Let me write it here because the comment isn't that all that clear. You have
$Var(y_{i}) = (h_{i}^{2} \times (b-a)^2/12) + \sigma^2$
From the data, you will have, the sample observations, ${y_{i}}$.
You know the mean of the right hand side. Check it but I think it's zero.
So, given that the mean is zero, this implies that
$ \sum var(y_{i}) = \sum_{i=1}^{N} [...
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Any hints?
sure!
hint 1
You can easily estimate the variance of $y_i$.
hint 2 & 2.5
You know the variance of $h_ix_i$ (hint: what does scaling with a scalar do to the variance of $x_i$?).
hint 3
What is the variance of a sum of random variables that are independent?
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