The occurrences of hurricanes that make landfall during the meteorological phenomenon “El Niño” are modeled as a Poisson process (Bove et al. (1998)). The authors claim that "During an El Niño year, the probability of two or more hurricanes making contact with the ground in the United States is 0.28 ”. Find the rate of Poisson process.
My approach:
Let the beginning of "El Niño" be $N_0=0$ and $N_1$ the end.
We know that $$P(N_1-N_0\geq 2) = 0.28$$
Now let's find $\lambda$ $$P(N_1-N_0\geq 2) = P(N_1 \geq 2)=1- P(N_1 < 2)= 1-2e^{-\lambda}(\lambda) $$
Then $$1-2e^{-\lambda}(\lambda)=0.28$$
Then $$\lambda=0.2738$$
I'm not sure if my approach is correct. Any suggestions would be great!