Given, for a fixed expiry T, the set of put prices for all strikes K : Put(K) we defined the implied distribution, pdf(u), as the density function for S(T) that satisfies this relationship for all K: Put(K)=exp(r(Tt))S0K(Ku)pdf(u)du Show that the E[S(T)] under this density function equals the forward price of the stock to delivery date T. Hint: First use this density to price out a forward contract with invoice price IP and delivery date T