E.g., I have this function $P = e^{-x} \frac{x^k}{k!}$ and I can't figure out how to evaluate $x$ If it's possible, please show me how. And if it's possible, is it possible with any equation?
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This equation gives you the probability of observing k independent events per given time period, if the average in that time period is x. So, what you can do is measure the number of events in a very long time period and then calculate the average number in that given time period. – Count Iblis Jun 17 '18 at 18:03
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It is not possible with all equations. In particular polynomials and exponentials do not play nicely together, so equations that mix them are often not soluble analytically. Sometimes the Lambert W function can help, but it doesn't leave me feeling enlightened as I know very little about its properties. You can often solve them numerically, but that may not help further on. – Ross Millikan Jun 17 '18 at 18:27