For my SIMULINK model I need to generate a signal that takes the values 1 or 0. To generate it I need to draw a number from a an exponential distribution and use this number as the time the signal stays in 0. Once this time has passed, I have to draw a new number from the exponential distribution and use this number as the time the signal stays in 1, and the repeat the process until the end of the simulation. As a SIMULINK newbie I'm quite puzzled by this problem and would appreciate any suggestions on how to solve it.
You've got a couple of choices.
In MATLAB, you can generate all samples in advance (i.e. before running the simulation) and use them to create a suitable signal, then use that as an input into the model (using the From Workspace block).
Or, if you need to do the sampling at each time step, then you have to write an S-Function, using the random number in the mdlGetTimeOfNextVarHit method. There is an example of doing something very similar on the Goddard Consulting web site called Square Wave with Jitter.