I'm new to this topic and I'm sorry if my question in basic.
Imagine a traffic light that starts working from 7 a.m. every morning, with the frequency of 1 minute green light and 3 minutes red light (it starts with green). Let the time you reach the traffic light be a random variable (if needed, $\lambda = \ln(2)$ ). If $Y$ is the time you wait at the traffic light, find the cumulative mass function for $Y$. also, the time you wait and the time you reach the traffic light is all in minutes.
what I have tried so far: exponential random should be used. the time we reach the traffic light then will be: $$F = 1 - e^{-\lambda*y} = 1 - 2^{-y}$$ but I'm not sure how to include the green or red light factor within the solution.