guys, I have a very ımportant question. First let me introduce parameters: $$S^A_1 = \text{first arrival of A event}, and S^B_1= \text{first arrival of B event}, and S^C_1=\text{ first arrival of C event}$$, then probability of $$P(S^A_1<S^B_1) = \frac {\lambda_A} {\{ \lambda_A + \lambda_B \} }$$, and I know how to derive this, also I know how to derive $$P(S^A_2<S^B_5)$$(adsbygoogle = window.adsbygoogle || []).push({}); BUTwhat is the probability of $$ P(S^A_1<S^B_1<S^C_1)$$ ????AND ALSOwhat is the probability of $$P(S^A_2<S^B_4<S^C_6)$$ ??? ıf you know could you show me thederivationof that probabilities????

I really endeavour to dig lots of things related to this situation out of internet, but I have not found worthy....

thanks in advance...

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# I N events occur in one Poisson process before m events

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