In nutritional studies, measuring individual’s anthropometric profiles such as body fat is important. Refer to both the body fat dataset and its readme fille available on Canvas. Consider two variables of percent body fat, using Brozek’s equation and Siri’s equation, respectively. Assume a bivariate normal distribution for this pair of variables.

(a) Obtain maximum likelihood estimates of the mean vector µ and the covariance matrix Σ.

(b) Use R software to draw the 3D density function.

(c) Use R software to draw the contour plot of this density.