Suppose an agent has $100. He opens a demand deposit of S100 with a bank which has asset x where x is a random variable. Required:
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?
b. Suppose changes in the economy changes the distribution of x. Now x is uniformly distributed on the interval [60, 200]. The density of x is f(x)=1/140 on [60, 200) and f(x)=0 otherwise. What is the expected loss of the depositor?
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.
d. 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 I=84. Calculate the expected loss of the depositor.