The $N(t)$ is a poisson process for the number of events to occur with a mean $\lambda(t) = 3$ per day. I am supposed to find the probability of more than 200 events in 60 days. My theoretical answer does not match the simulations in R, what is wrong?
My calculation is
$$ P(N(t) > 200 | T = 60) = 1 - \int_0^{60} \frac{(3 t)^{200}}{200!} \times e^{-3t} dt = 1 - 0.021 \approx 0.98. $$
Simulations of a 100 processes in R gives a number of 6/100 = 0.06. That is 6 events out of 100 being more than 200. What am I not understanding?