Hey everyone, first, let me say I understand the complement rule. Where I am confused is over the integration. My professor said that suppose you have a continuous cumulative distribution function F(x) = 1-e(adsbygoogle = window.adsbygoogle || []).push({}); ^{-x/10}, if x > 0 (0, otherwise). And suppose you want to find P(X>12) you can use the complement rule 1-P(X<=12). Which is equivalent to 1-F(12) [note he said this works for all cases, not just this example].

My question is why isn't it 1-[F(12) - F(0)]?

This is really tripping me up. If your x can take all probabilities from 0 to 12, don't you want to find the area from 0 to 12 and not just F(12)?

I know this is a method of simplifying the integral since you have an improper integral and have to evaluate a limit (supposing you don't use the compliment rule). But why does this work for all cases?

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# I Confusion over using integration to find probability

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