Consider a gamble x with pdf given by f(4) = 0.75 and f(16) = 0.25.

a. Calculate E(x) and Var(x).

b. Suppose Siqi has expected utility preferences with u(x) = x. What is her Eu(x)?

c Suppose Ritesh asks Siqi if she'd rather take x or a fixed $4 payment. Which will she pick?

d Consider a used car market from Questions 21 & 22, where each car has quality q that ranges from $0 to $10,000. All quality levels are equally likely. Sellers value their car at q while buyers value each car at q + 400. Only the seller knows q, not the buyer. Find the market price p in this market, and describe which cars will be for sale