1. A policy will cover 80% of all losses in excess of 100, with the further provision that a maximum payment of 900 will be made regardless of the amount of the loss. Express the amount paid on a claim with terms of the form X ∧ d.
2. If N takes values 0, 1, 2, 3 with probabilities 0.5, 0.3, 0.1, 0.1 respectively, and X takes values 1, 2, 3, 4, 5, 6 with probabilities 0.2, 0.2, 0.2, 0.2, 0.1, 0.1 respectively, find the probability that S = 6.