Greetings I have a Bernoulli process question as follows:
You are waiting at a bus stop and there are two kinds of buses stopping there: Bus A and Bus B. Each arriving bus is Bus A with probability 0.75, independenly from one arrival to the next. Note that we can model this as a Bernoulli process.
a. You would like to take Bus B, and show up at the bus stop at a random time. How many buses on average will arrive before you can get on one?
b. Find the expected number of Bus A arrivals between two consecutive Bus B arrivals?
c. You arrive at a random time. What is the expected number of Bus A arrivals between Bus B you get on and the previous Bus B?
I am particularly stuck at a and c and any help is appreciated.
Re: Bernoulli Process
Hint (to start you off): What is the formula for the expectation of a discrete random variable? If the probability of getting on a bus is p then 1/p will be the number of times you would expect to wait: can you explain why you think this is the case?