Question 2. Clustering [35 points) Suppose that we have six points $\mathrm{x}_{1}, \ldots, \mathrm{X} 5$ with following distance matrix: \begin{tabular |11111111111111} Whline & $\mathrm{X}_{i}$ & $\mathrm{X}_{2}$ & $\mathrm{X}_{3}$ & $\mathrm{X}_{4}$ & $\mathrm{X}_{5}$ & $\mathrm{X}_{6}$ Whline $\mathrm{X}_{1}$ & 0 & $0.24$ & $0.22$ & $0.37$ & $0.34$ & $0.236 Vhline $\mathrm{X}_{2}$ & & & $0.15$ & $0.20$ & $0.14$ & $0.25$ \hline $\mathrm{X}_{3}$ & & & & $0.15$ & $0.28$ & $0.11$ Vhline $\mathrm{X}_{4}$ & & & & 0 & $0.295 & $0.22$ Whline $\mathrm{X}_{5}$ & & & & & & $0.39$ Thline $\mathrm{X}_{6}$ & & & & & & 0W Whline \end{tabular) a) Using the distance matrix above, sketch the dendrogram that results from hierarchically clustering these points using complete and average linkage. Clearly label your dendrogram and include all merging distances. b) Suppose we want a clustering with two clusters (ignore singletons). Which points are in each cluster for average linkage? SE.SD.027