After being caught in an embarrassing high-profile data fabrication scandal, Calambya University decides to stop sharing data with the national college ranking organization, effective in 2023. Rival school Mahogany University is overjoyed and offers each student a tuition refund worth X thousand dollars, where X=Calambya’s 2023 Ranking−Mahogany’s 2023 Ranking. One Mahogany student, Justin, offers to sell the following contract to his friend Kevin for 0.70 thousand dollars, before X is known: Justin will give Kevin the right but not the obligation to purchase Justin's tuition refund for only 0.5 thousand dollars. Suppose X∼Exp(β), where β is the scale. Compute β to the nearest tenth under the assumption that the contract is priced fairly.
