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9. Consider the sample data D : {0, 1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 4, 5}. Answer the following ques tions by using the parametric and nonparametric density estimation methods covered in the class. (a) Compute the histogram density estimates for the values :r: = 2 and a: = 4. Assume that the desired number of bins is N : 6 and the bins are centered at {0, 1, 2, 3, 4, 5}. (b) Compute the kernel density estimates for the values a: = 2 and a: = 4 by using the following kernel function: (Assume that the smoothing parameter is given as 2.) KW): (1-lul)1(JUI S 1) (c) Now, assume that the distribution of our data is a member of a parametric fam ily, namely a Gaussian. Compute the maximum likelihood estimate of the density parameters using the sample data D. (d) Plot the histogram, kernel and the maximum-likelihood estimated Gaussian density estimates. Describe how they capture the data in terms of smoothness of the density function and tness to the sample data D