Suppose the four variables being used are denoted by X1,...,X4. Use the sample covariance matrix to estimate the variance of 0.5X1 + 0.3X2 + 0.2X3. (Useful R facts: “t(a)” is the transpose of a vector...

Suppose the four variables being used are denoted by X1,...,X4. Use the sample covariance matrix to estimate the variance of 0.5X1 + 0.3X2 + 0.2X3. (Useful R facts: “t(a)” is the transpose of a vector or matrix a and “a %*% b” is the matrix product of a and b.)

 Fit a multivariate-t model to the data using the function cov.trob in the MASS package. This function computes the MLE of the mean and covariance matrix with a fixed value of ν. To find the MLE of ν, the following code computes the profile log-likelihood for ν.