Question: 11. Let X denote a geometric random variable with probability of success p. a. Show that for a positive integer a, P(X > a) =

11. Let X denote a geometric random variable with probability of success p. a. Show that for a positive integer a, P(X > a) = q\" . b. Show that for positive integers a and b, P(X>a+b|X>a)=qb=P(X>b). This property is called the memoryless property of geometric distribution. Prove that Zle p)x_1p = 1 Prove thatE[X] = 1/19 Prove that Var[X] = (1 p)/p2 t Prove that MX (t) = 75:09: wraps\

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