Geometric Random variables ·In general, P=k) P(X=k X>a)= P(X>a) (1-p)k-1p (1-p)k-1p 28=a+1(1-p)k-1p 1 1 (1-p)a.T-1-p) =(1-p)k-a-1p =px(k-a) 4Geometric Random Variables • In general, 𝑃 𝑋 = 𝑘 𝑋 > 𝑎 = 𝑃(𝑋 = 𝑘) 𝑃(𝑋 > 𝑎) = (1 − 𝑝) 𝑘−1𝑝 (1 − 𝑝) 𝑘−1𝑝 ∞ 𝑘=𝑎+1 = (1 − 𝑝) 𝑘−1𝑝 𝑝(1 − 𝑝) 𝑎∙ 1 1 − (1 − 𝑝) = (1 − 𝑝) 𝑘−𝑎−1𝑝 = 𝑝𝑋(𝑘 − 𝑎) 4