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Two independent events A and B follow exponential distribution with parameter L: f(t)=Le^(-Lt) for t>=0. If X is the time where A occurs and Y the time where B occurs, calculate the probability P[X>=2*Y] meaning that A happens at least after double the time that B occurred.

How do I proceed? I need to integrate f(t) in the area where x>=2*y. Does that mean that 0<=y<=x/2?

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  • $\begingroup$ Random variables can follow exponential distribution but not events. $\endgroup$ – Kavi Rama Murthy Apr 10 at 9:56
  • $\begingroup$ Correct. Thank you. $\endgroup$ – EmKal Apr 10 at 11:05
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Assuming $X$ and $Y$ to be random variables, you need to integrate the joint distribution of $(X,Y)$ which is easy to compute as they are independent. Your integral limits are fine: $0\leq x<\infty, 0\leq y\leq x/2$. I think the final answer is $1/3$.

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  • $\begingroup$ Indeed, although using $0\leq y\leq \infty, 2y\leq x\leq \infty$ might be slightly easier to handle. $\endgroup$ – Graham Kemp Apr 10 at 10:21
  • $\begingroup$ Worked like a charm, thank you. $\endgroup$ – EmKal Apr 10 at 12:19

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