I am about to set up a meeting time with a famous composer. But this writer is often late for an appointment time. I take the maximum time this the writer is late as a random variable(θ) and try Bayesian inference.

1. Those who have met the writer in the past say that the artist arrives within as much as three hours.
2. I had a meeting with this writer once, and the writer came X hours later (but less than 3 hours). And based on this, I want to find the probability distribution of the newly θ obtained!