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1. obviously the cumulative density function of an exponential function reaches one but how do you use this to explain why a probability ( say P(X>8) ) can be equal to a conditional probability ( say P(X>16|X>8) ) ?
2. (Original post by championhopper)
obviously the cumulative density function of an exponential function reaches one but how do you use this to explain why a probability ( say P(X>8) ) can be equal to a conditional probability ( say P(X>16|X>8) ) ?
I don't see that you can. The relation P(X > a) = P(X > a+b | X > b) is only true for an exponential distribution, but the cumulative density function reaches 1 for any random variable, not just an exponential one.

In practical terms, calculate p(X>8) and p(X>16) and show p(X>8) = p(X>16)/p(X>8). (Standard conditional probabiltiy in other words).

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Updated: August 22, 2007
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