Jochem
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 May 12 accepted How does the rewriting of the following two equations work? May 12 revised How does the rewriting of the following two equations work? Made it completer May 12 suggested approved edit on How does the rewriting of the following two equations work? May 12 comment How does the rewriting of the following two equations work? Thank you. Just went through the same line of thought with @Potato. May 12 awarded Scholar May 12 awarded Supporter May 12 comment How does the rewriting of the following two equations work? Thank you. It is now clear to me! May 12 comment How does the rewriting of the following two equations work? This part I understand: $$(\lambda+\mu)\frac{\lambda}{\mu}P_0 = \lambda\frac{\lambda}{\mu}P_0 + \mu\frac{\lambda}{\mu}P_0$$ But when you add them up you get: $$\frac{\lambda * \lambda}{\mu}P_0 + \frac{\mu * \lambda}{\mu}P_0$$ Is it here that multiplying of the $$\mu$$ in the second part results in $$P_0$$? May 12 revised How does the rewriting of the following two equations work? added 7 characters in body May 12 comment How does the rewriting of the following two equations work? I recall that, but then you would expect that somewhere you get a value along the lines this would result in: $$\frac{\lambda^2}{\mu}P_0 + \lambda P_0 + \mu P_0$$ May 12 asked How does the rewriting of the following two equations work? May 8 awarded Cleanup May 8 awarded Editor May 8 revised Simultaneously solving of equations rolled back to a previous revision May 8 revised Simultaneously solving of equations added 24 characters in body May 8 asked Can anybody recommend a comprehensive source for understanding mathematical notations? May 8 comment Simultaneously solving of equations @Amzoti This looks promising. I struggle a bit to understand your first step. What procedures did you go through to solve reach variable by using 1 = w + x + y + z? Did you do the following: w = 0.080w + 0.632x + 0.264y + 0.080z, which leads to 0 = 0.080w - w + 0.632x + 0.264y + 0.080z. Then add 1 = w + x + y + z to 0 = -0.920w + 0.632x + 0.264y + 0.080z and this leads to 1 = 0.08w + 1.632x + 1.264y + 1.080z. Is that the procedure you did for every line? May 7 comment Simultaneously solving of equations @GitGud The reason why the numbers are ugly is due to the fact that it comes from a markov matrix and the equation needs to be solved to obtain the stead-state probabilities of the transition matrix. As it all needs to add up to 1, things get ugly. May 7 awarded Student May 7 asked Simultaneously solving of equations