4. Fit the normal mixture model to the galaxies data in MASS library.

(a) [5pt] Find the number K of mixture components using BIC and the MLE of parameters. (b) [5pt] Given the above estimator, evaluate the density at x = 20000.

4. Fit the normal mixture model to the galaxies data in MASS library. (a) [5pt] Find the number K of mixture components using BIC and the MLE eters. (b) [5pt] Given the above estimator, evaluate the density at r = 20000. 4. Fit the normal mixture model to the galaxies data in MASS library. (a) [5pt] Find the number K of mixture components using BIC and the MLE eters. (b) [5pt] Given the above estimator, evaluate the density at r = 20000