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Aug 2, 2017 at 16:46 history edited user44143 CC BY-SA 3.0
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Aug 2, 2017 at 16:10 comment added user44143 Brute force will get you formulas, but not nice formulas. It took substantial tinkering with Mathematica results to get something readable. Maybe tinkering with the n=4 case will make a generalization obvious. Try Probability[ a x + b y < d, {x [Distributed] ExponentialDistribution[lambda], y [Distributed] ExponentialDistribution[lambda]}] and the like, but beware that this command for two dimensions gives a result with 13 cases before tinkering!
Aug 2, 2017 at 15:58 comment added gradstudent Thanks! Are these obtained by some brute force computation like just doing iterated convolutions or are there tricks to quickly generalize this to $n-$dimensions?
Aug 2, 2017 at 14:56 history edited user44143 CC BY-SA 3.0
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Aug 2, 2017 at 14:45 history answered user44143 CC BY-SA 3.0