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In general, if the distribution is not specified, go with the Beta distribution on the exam.
It is perfectly normal that the two distributions will provide the same answer if you have pessimistic and optimistic values which are equidistant from the most likely.
the values are determined by the equation M = (P+O)/2, which is the same as Kiron mentioned with equidistance from the most likely M, which then is also the mean.
As somebody training into statistics (one of my grades are "licenciado en estadística" which I think is the same than bachelor major on statistics) my recommendations is going to the definition of the function that best caracterized the activity distribution. And let me say: if you are using things like PERT it has no sense to spend too much time on this. To justify or understand that go to for PERT definition mainly why the normal distribution is the best approach to take taking into account the inherent errors.
Thanks for your contributions.
I got the idea.
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