Geometric Random variables 。In general,, P(X=k) PX=k X>a= P(X>a) (1-p)k-1p (1-p)k-1p 2R=a+1(1-p)k-1p 1 1 (1-p)a.1-(1-p) =(1-p)k-a-1p =px(k-a)Geometric Random Variables • In general, 𝑃 𝑋 = 𝑘 𝑋 > 𝑎 = 𝑃(𝑋 = 𝑘) 𝑃(𝑋 > 𝑎) = (1 − 𝑝) 𝑘−1𝑝 σ𝑘=𝑎+1 ∞ (1 − 𝑝) 𝑘−1𝑝 = (1 − 𝑝) 𝑘−1𝑝 𝑝(1 − 𝑝) 𝑎∙ 1 1 − (1 − 𝑝) = (1 − 𝑝) 𝑘−𝑎−1𝑝 = 𝑝𝑋(𝑘 − 𝑎) 4