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If the exponential distributions have the same scale parameter it's known as the Erlang-2 distribution. PDF and CDF exist in closed-form but the quantile function does not.

If you're looking to generate random variates the easiest method is to sum exponentially distributed variates. If the scale parameter is the same you can simplify a bit: -log(U0) - log(U1) = -log(U0*U1).

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Q: What is the distribution of the sum of two exponentially distributed random variables?
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