 Solution

The fitted LDA rule replaces ${\pi }_l,{\mu }_l,\Sigma$ by class proportions, class sample means, and the pooled within-class covariance, then maximizes the resulting ${\hat{\delta }}_l(x)$. Means and covariances have unbounded sensitivity, so a gross outlier can substantially move every LDA boundary. A soft-margin linear support vector machine uses hinge loss; observations beyond the correctly classified margin cease contributing, though mislabeled or extreme points can still matter according to the penalty $C$. Thus the SVM is generally more robust to well-classified extremes, while neither method is automatically robust to adversarial outliers.