Assume that the system at hand has a set of users M = {M1, M2, ...., Mn} and each Mi has a probability of creating an event e.g., M1=0.3, M2= 0.1, where the total probability for all users =1. The system allows all users to create events with a rate (e.g., mean rate is 10 seconds), that means on average each 10 seconds an event will be created by a user.
I tried to use exponential distribution with rate = 10, and then i draw a random number (0-1) and run a probability check to assign a user to the event. e.g., if random number <= 0.3, assign it to M1 ; if it is between 0.31 and 0.40, assign it for M2 etc.
Since my math is not good, is there any better solution to such system? also, is there any way to know how long (on average) it takes each user to create an event (taking into account only 1 event each 10 seconds on average)?