What distribution is the most appropriate? I am given the following problem:

A student S wants to take the tram to go home after his lectures are
over. The tram line he’s used to take leaves every 7.5 minutes on
average at the university. Unfortunately, student S cannot remember
the departure times. Thus, he always arrives randomly at the tram
station every single weekday.

I am then asked the question which distribution is the most appropriate one to model the daily waiting times of the student.
The random variable $X$ reflects the daily waiting time. I thought about an uniform distribution with $a=0$ and $b=7.5$ since the student arrives randomly at the tram station and thus has equal probability for every waiting time between $0$ and $7.5$.
So far so good. What is confusing me though is the fact that the arrival of the tram is again a random variable (the tram only arrives every 7.5 min on average). So I am not exactly sure how to model this as the upper bound $b$ of the uniform distribution would not always be exactly $7.5$  but rather a realisation of the underlying distribution.
I hope someone can explain how I can model this accurately.

I guess the problem assumes that you'll use the exponential distribution for the waiting time, P(next tram time > t) = 1/(average time) * exp(-t / average time). This is equivalent to saying that tram arrival times follow Poisson process. And then use a memory-less quality of the exponential distribution which is P(next tram time T > a + b | T > a) = P(T > b), i.e. if a tram did not arrive by time a, probability to wait for another b minutes is the same as it was at the beginning. In survival processes exponential distribution is used for a constant hazard - the probability of a tram to arrive at each particular time is the same and does not depend on how much time it was from the last one. In your problem terms, if a student comes at a random time, independent from T, the waiting time distribution will be the same as if a person arrived right after the last tram, and expected to wait the full 7.5 minutes.
Intuitively, if the trams come exactly every 7.5mins, a student will on average wait for 7.5/2 minutes, but as they come randomly and there will be times when the waiting time is long, the average waiting time may be quite long - in case of poisson/exponential distribution, the residual waiting time is at par with non-shifted expected time, however Weibull distribution for example will yield different results, you'd need to use jbowman's density approach to find what it is.
Also, check out this post on this problem
https://jakevdp.github.io/blog/2018/09/13/waiting-time-paradox/ or this one Please explain the waiting paradox
