Question 3 Geometric and Exponential Distributions. Let X m GeomtIp} be a geometrically-distributed random variable. {a} Find the distribution function Fx(}. [b] Show that, for positive integers o and ii, PI[X \":3 o + Ei|X is o) = P(X 2:- b}. {This property is called the memoryiess property.) Let Y ~ Emp} be an exponentially-distributed random variable. {c} Find the distribution function Fy} and nd the median of Y as a function of ,8. (Hint: P{Y g med{Y}) = 0.5}. {d} Let V be random variable distributed as a \"shifted exponential distribution\" which has density fvu} = %EEi} for u 2 :1. Find Er'}. (Hint: you may integrate from the density directly, or write V as a function of Y)