We consider the polar corrdinates in which (by mapping theorem),  raindrops are a point process with $\lambda r$ $drops/cm$
~~
$$
\begin{align}
P[\Lambda^1([0,r] \times [0, 1] \times R^2)=0] &=exp(-\int_{0}^r \int_{0}^{1} \int_{R^2}\lambda p(x,y)dxdydtdr)\\ &= exp(-\lambda t 2\pi \int_0^r \rho e^{-\rho}d\rho)\\
&= exp(-\lambda t 2\pi(1-e^{-r}(r+1)))\\
\end{align}
$$
~~

d6e1691a91ac623e4fed2238bf60cd1a50d14874
ipynb
Jupyter Notebook
2015_Fall/MATH-578B/Homework3/Untitled.ipynb
NeveIsa/hatex
c5cfa2410d47c7e43a476a8c8a9795182fe8f836
MIT
2015-09-10T02:45:33.000Z
2022-02-10T03:20:47.000Z
2015_Fall/MATH-578B/Homework3/Untitled.ipynb
NeveIsa/hatex
c5cfa2410d47c7e43a476a8c8a9795182fe8f836
MIT
2015-09-16T23:11:00.000Z
2015-09-23T21:21:52.000Z
2015_Fall/MATH-578B/Homework3/Untitled.ipynb
saketkc/hatex
c5cfa2410d47c7e43a476a8c8a9795182fe8f836
MIT
2015-09-25T19:06:45.000Z
2022-02-10T03:21:09.000Z
Qwen/Qwen-72B
1. YES
2. YES