1. The amount of a policyholder's loss (X) is assumed to follow a uniform distribution on the interval (0,2000). Consider the following insurance on X: (i) There is an ordinary deductible of 800 per loss. (ii) If X is between 800 and 1200 , the insurance pays the excess of X over 800. (iii) If X is greater than 1200 , the insurance pays 400 plus 80% of the excess of X over 1200 . Calculate the expected insurance payment for a loss. [Hint: first, determine an expression for the insurance payment in terms of X. The expression will depend on which of the three above ranges of X is being considered. The expected insurance payment will be the sum of integrals involving the density function of X.] 1. The amount of a policyholder's loss (X) is assumed to follow a uniform distribution on the interval (0,2000). Consider the following insurance on X: (i) There is an ordinary deductible of 800 per loss. (ii) If X is between 800 and 1200 , the insurance pays the excess of X over 800. (iii) If X is greater than 1200 , the insurance pays 400 plus 80% of the excess of X over 1200 . Calculate the expected insurance payment for a loss. [Hint: first, determine an expression for the insurance payment in terms of X. The expression will depend on which of the three above ranges of X is being considered. The expected insurance payment will be the sum of integrals involving the density function of X.]