Primal-Dual Algorithm ·Pick∈[O,1]uniformly at random. Suppose t is the first day that>=ixj≥， then rent in all days before t and buy on day t. ●Facts: -Rental probability 1- Buying probability:>=1=xPrimal-Dual Algorithm • Pick 𝛼 ∈ [0,1] uniformly at random. • Suppose 𝑡 is the first day that σ𝑗=1 𝑡 𝑥𝑗 ≥ 𝛼, then rent in all days before 𝑡 and buy on day 𝑡. • Facts: – Rental probability : 1 − σ𝑖=1 𝑗−1 𝑥𝑖 = 𝑧𝑗 – Buying probability: σ𝑗=1 𝑡 𝑥𝑗 = 𝑥