Hi

I am really stuck with some parts of this question, and some I think I've got. I can't get my head around this

A bank has a central queue served by four assistants - two of the four assistants are exponentially distributed with mean 4 minutes, the other two exponentially distributed with mean 6 minutes.

When I enter the bank all 4 assistants are busy, but no-one is waiting to be served.

Q1. Find the distribution of the time I have to wait before I can move forward for service, hence show my expected waiting time is 72 seconds

I have got as far as $\displaystyle \sim M(\frac{1}{4} + \frac{1}{4} + \frac{1}{6} + \frac {1}{6})$ or $\displaystyle M(\frac{5}{6})$ but I have no idea how to show the expected waiting time is as above.

Q2. Calculate the probability that I have to wait more than 1 1/2 minutes until an assistant is free to serve me.

I think I've got this one...

$\displaystyle P(X>1.5) = e^{\lambda.x}$ where $\displaystyle \lambda = 5/6$ and $\displaystyle x = 1.5$ giving me 0.287

Any help would be very much appreciated