$2)$ Consider a futures contract, which is currently valued at zero, but has the true value of either $+1$ or $-1$ with equal probabilities. The market is cleared by a risk neutral competitive market maker who posts a bid price at which he is prepared to buy one unit of the contract from a seller, and an ask price at which he is prepared to sell one unit to a buyer. The market maker believes there is $80\%$ chance the next trader is an uninformed trader who is equally likely to buy or sell one unit for liquidity reasons, and $20\%$ chance the next trader is an informed trader who trades on the basis of his or her $($perfect$)$ information about the true value of the futures. Work out the bid and ask prices for the next transaction.