Probability of a multiple variables sum

#1
Hi everyone,

I’m coming here for really advance statistic/probability advice.
I would like to know the probability of a variable TAU_total such as TAU_total=TAU1+TAU2+….+TAU129.
The variables TAUi are independent of each other.
For each one of them, I have a sample of 20,000 values which you can see some examples of their distribution on the histograms in the attachment.
My question is the following: I would like to be able to determine the probability of TAU_total to be superior to a certain value Xmax.

Thank you for your help,
Regards,
Rémy
 

Attachments

#2
Try a Monte Carlo approach. Take one of the 20000 values at random for each tau. Add them up. Write down the answer. Repeat 10000 or so times. See where xmax fits into the distribution of totals. kat