Independent solution

How to solve this Poisson Distribution question

Setup

Setup

Use the Poisson probability at zero to recover the mean parameter.

Pr⁡(X=0)=e−λ=0.18\Pr(X=0)=e^{-\lambda}=0.18

Model

Model

Take logarithms and identify the interval containing the parameter.

λ=−ln⁡(0.18)=1.7147984281…\lambda=-\ln(0.18)=1.7147984281\ldots
1<λ<21<\lambda<2

Compute

Compute

For a noninteger Poisson mean, the unique modal count is the greatest integer below the mean.

mode⁡(X)=⌊λ⌋=1\operatorname{mode}(X)=\lfloor\lambda\rfloor=1

Answer

Answer

The most likely count is 1.

1(B)\boxed{1\quad\text{(B)}}