Statement I is accurate because it correctly describes the payoff from a long put option. In options trading, a long put option gives the holder the right to sell a specified quantity of an underlying asset at a specified price (the strike price) within a fixed period of time. If the current price of the stock is less than or equal to the strike price (Sₜ ≤ X₁), the put option is in-the-money, and the holder would exercise the option to sell at the higher strike price rather than the market price, resulting in a payoff of X₁ − Sₜ.

Statement II is incorrect. If the current price of the stock is greater than the strike price X₃ (S > X₃), the long put option is out-of-the-money, and the holder would not exercise the option because they could sell the stock at a higher market price in the market. In this case, the payoff from a long put option is zero, not X₃ − Sₜ. A payoff of X₃ − Sₜ would be negative (since S > X₃), which is not possible for a long put option since the maximum loss is limited to the premium paid.