Let Y denote a geometric random variable with probability of success p. (a) Show that for a positive integer a, PCY > a)

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Let Y Denote A Geometric Random Variable With Probability Of Success P A Show That For A Positive Integer A Pcy A 1 (44 KiB) Viewed 177 times

Let Y denote a geometric random variable with probability of success p. (a) Show that for a positive integer a, PCY > a) = 0 PCY > a) = Σ y = a + 1 = - q X = 1 (b) Show that for positive integers a and b, PIY> a + b[Y> a) = 96 = P(Y>b). PCY> a + b[Y>a) PY > a+b) P(Y>a) a qe This result implies that, for example, P(Y> 7Y> 2) = P(Y > 5). Why do you think this property is called the memoryless property of the geometric distribution? The geometric distribution values are the same for all numbers. Only future outcomes matter to the geometric distribution. Only past outcomes matter to the geometric distribution. (c) In the development of the distribution of the geometric random variable, we assumed that the experiment consisted of conducting identical and independent trials until the first success was observed. In light of these assumptions, why is the result in part (b) "obvious"? The results in the past are not relevant to a future outcome (dependent trials.) The results in the past are relevant to a future outcome (dependent trials.) The results in the past are not relevant to a future outcome (independent trials.) The results in the past are relevant to a future outcome independent trials.)