Exponential distribution probability example If the expected time until a neutrino appears in 1 minute follows an exponential distribution with mean 1, what is the probability that no neutrinos arrive in two minutes?
So the density would be $\lambda e^{-\lambda x}$ where $\lambda=1$, from here to get the $P(X\leq x)$ you take $\int_0^x e^{-x} dx = 1-e^{-x}$. I have no idea where I would go from here. Would I do $1-P(X\leq 2)$? The whole exponential distribution doesn't really make sense to me.

This problem need to be solved by Poission Process.
Let $N_t$ denote the number of neutrinos upto time $t$. 
It is well-known that $N_t\sim Poi(\lambda t)$ 
So the required probability $$P(N_2-N_0=0)=P(N_2=0)=e^{-2}$$
Disclaimer: I have assumed that by $2$ minutes, you meant the first $2$ minutes.
If not, notify me, I will change the answer accordingly.
