A 10-year endowment insurance issued on (50) pays $2000 at the end of the month of death if (50) dies during the 10-year term, or pays $1000 at maturity. Assume that = 0.06 and l_x = 100 x for 0 x 100.

(a) Write the expression for the present value random variable Z of the benefits in terms of K ⁽¹²⁾₅₀ . [2 pts]

(b) Calculate E[Z]. [4 pts]

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