Question

Let X Geom(p). For positive integers n, k define P(X = n + k | X...

Let X Geom(p). For positive integers n, k define

P(X = n + k | X > n) = P(X = n + k) / P(X > n) :

Show that P(X = n + k | X > n) = P(X = k) and then briefly argue, in words, why this is true for geometric random variables.

Math   Statistics-And-Probability   
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Answer #1

As geometric distribution is defined as number of trails needed to get the first success. Hence, it does not depends on the past trails whether the next outcome is a success or not, that is, geometric distribution has memoryless property. This is why the above result is true for geometric distribution.

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