I know that you can combine two normal pdfs and result in a normal distribution with the sum of the means and similar for the standard deviation.
In the case of an exponential distribution what is the procedure. In regards to waiting time where the two samples occur in succession how would i go about combining that in regards to a total wait time. Would this total time be an exponential still and would the mean simply be the sum of the means?
Finally if I were to use this to approximate a probability, is there an exponential approximation to a normal or would I simply use this new distribution to calculate the probability?