I'm a little confused about this question I was given:
"Calls arrive at a tech support center with a mean of 4 per hour. Assuming the number of calls received in 1hr is described by a Poisson distribution, find the probability that there is more than 20 min between the arrivals of randomly selected successive calls.
λ = 4, but since it is exponential, it is 1/4. The formula I think I need is \int_0^w \lambda e^{-\lambda t} dt
◂∫▸ ∫ 0 w λ ◂◽˙▸ e − λ t d tbut I cant figure out what my w should be.
Call $X=\text{number of calls per twenty minutes}$. That $X$ is Poisson-distributed with $\lambda=4/3$. Compute $P(X=0)$.