Hi I'm having some problems with combining exponential distributions.

Suppose we have a single server, fifo queue. Arrivals and service times are distributed exponentially - we can then work out info like variance, standard deviation and expected response time quite easily.

However, now say customers can be divided into two types - 1/3 long and 2/3 short service times, with each group having service times exponentially distributed with a different lambda. how do i combine the two groups to get the same information?

Thanks very much for any help