Solution
= Solution
Mark a virus at distance $r\le R$ if its uniform radius exceeds $r$, with probability $1-r/R$. Marked Poisson thinning gives a Poisson count with mean
$$
\boxed{2\pi\lambda\int_0^Rr(1-r/R)dr=\lambda\pi R^2/3.}
$$
= Solution
Mark a virus at distance $r\le R$ if its uniform radius exceeds $r$, with probability $1-r/R$. Marked Poisson thinning gives a Poisson count with mean
$$
\boxed{2\pi\lambda\int_0^Rr(1-r/R)dr=\lambda\pi R^2/3.}
$$