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{\bf Nonparametric Statistics Homework VI.}\\
Due date: December 10 2:30pm. $1\%$/hour deduction afterward.
Worth $6\%$ of your final grade.\\
\begin{enumerate}


\item Using the Cavendish data, estimatethe the probability density of the measurements using spline. Compute the expected density of the earth. Test if the density of earth is 5.46. What is the P-value? Hint: you may need to generate bins and smooth the bin heights with splines. The data file is at\\
http://www.stat.wisc.edu/~mchung/teaching/data/earth.data.

\item Do Problem 1 with using Fourier series expansion.

\item Let $Y_1=0,Y_2=2,Y_3=-1,Y_4=4$. Find cubic curve $\mu(t)$ that minizes
$$\frac{1}{4}\sum_{i=1}^4 \big(Y_i-\mu(i)\big)^2 + \lambda \int_{1}^4 \mu^{''}(t) \; dt$$
for $\lambda =0, 1$ and 1000 (warning: MATLAB cublic spline minimizes a slightly different
function).
\end{enumerate}
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