Poisson distribution - daisies

The meadow behind FLD was divided into 100 equally large parts. Subsequently, it was found that there were no daisies in ten of these parts. Estimate the total number of daisies in the meadow. Assume that daisies are randomly distributed in the meadow.

Correct answer:

n =  230

Step-by-step explanation:

$$\begin{gathered} S=100 \\ {p}_0=\frac{10}{S}=\frac{10}{100}=\frac{1}{10}=0.1 \\ x=0 \\ {p}_0=P(X=0)=\frac{{\lambda }^x}{x!}\cdot e^{-\lambda } \\ {p}_0=1/0!\cdot e^{-\lambda } \\ {p}_0=e^{-\lambda } \\ \ln p_0=-\lambda \\ \lambda =-\ln (p_0)=-\ln 0.1\doteq 2.3026 \\ {n}_1=S\cdot \lambda =100\cdot \lambda \doteq 230.2585 \\ n=[n_1]=[230.2585]=230 \end{gathered}$$

Try another example