Question

Stats: Students enter a library on the average of 2 every 3 minutes. The waiting time until the first student arrives can be modeled by an exponential random variable. How do I calculate the probability that it less than 3 mins for the first student to arrive?

Answer 1

with \( \lambda \)=2 arrivals every 3 minutes
the probability of an arrival in t minutes is
\[ P(t)= 1-e^{- \frac{2}{3}t} \]