In a single-period market, there are two securities initially priced at S = $1,S2 = $4. For period one, there are three possible world states N = {w, W2, W3}, where the securities are expected to have the corresponding values: S} (@) = $1 S (W) = $3 S (W3) = $5 S () = $0, si (w) = $1, S (W) = $1, a. Is this market arbitrage free? Explain your reasoning. b. A bank is planning to introduce a risk-free bond in this market. The bond has an initial value of $3, and an interest rate r, i.e., by buying one bond at time 0, you will make $3(1 + r) at time 1. For what values of r, can this bond be introduced into to the market without creating an arbitrage opportunity. Explain your reasoning.