1. Show that \(\displaystyle E(X^2) = 2\Theta\) and than construct unbiased estimator of parameter \(\displaystyle \Theta\) based on \(\displaystyle \sum_{k=1}^n X_k^2\)

2. Estimate parameter \(\displaystyle \Theta\) from following \(\displaystyle n=10\) observations:

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`16.88 10.23 4.59 6.66 13.68 14.23 19.87 9.40 6.51 10.95`

**1.**I have just plugged in 2 theta in Rayleigh's variance formula and it evaluates to true, but I'm not sure about correct way of constructing unbiased estimator \(\displaystyle \hat{\Theta}\)

\(\displaystyle Var(X)=E(X^2) - E^2(X)\)

\(\displaystyle Var(X)=2\Theta - E^2(X)\)

\(\displaystyle \frac{4-\pi}{2}\Theta=2\Theta - \sqrt{\Theta\cdot\frac{\pi}{2}}^2\)

\(\displaystyle 4\Theta - \pi\Theta = 2(2\Theta - \frac{\pi\Theta}{2})\)

\(\displaystyle \Theta = \Theta \)

**2.**I need help with this one