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Question 4 [12 points] Suppose an agent has $100. He opens a demand deposit of $100 with a bank which has asset x where X is a random variable. a) Suppose x is uniformly distributed on the interval [100, 200]. The density of x is f(x):1/ 100 on [100,200] and f(x):0 otherwise. What is the expected loss of the depositor? [2 Points] b) Suppose changes in the economy changes the distribution of X. New X is uniformly distributed on the interval [60, 200]. The density ofx is f(x):1/ 140 on [60, 200] and f(x):0 otherwise. What is the expected loss of the depositor? [3 Points] c) Suppose X is uniformly distributed on the interval [0, 200]. The density of X is f(x):1/200 on [0, 200] and f(x):0 otherwise. Calculate the expected loss of the depositor. [3 Points] (1) Suppose x is uniformly distributed on the interval [0, 200]. Given the macroeconomic environment, the government introduces deposit insurance. There is deposit insurance of an amount I280. Calculate the expected loss of the depositor. [4 Points]