I have a Poisson distribution with λ = 10, which is the responses over 5 business days (Monday - Friday inclusive), with the probability constant through the week.
What would be the probability the first response comes on Tuesday? I am thinking since all events are independent and the probability is constant on every day, it would just be Poisson distribution of P(X=1).
HINT: If I understand correctly, I would say that
X ~ number of events per business day (integer random variable $\ge 0$, Poisson distribution with the parameter $\lambda_1=\lambda/5$).
Then
P(X=0) = the probability no event on Monday,
P(X>=1) = the probability on Tuesday at least one event.
This must be true at one stroke.