Suppose an illness case during a single month has a poisson distribution with parameter $\displaystyle \mu$.

The number of cases in January and February are 1 and 3 respectively.

How can I find the likelihood function for this case?

Following is my working: $\displaystyle e^{-\mu}\mu*\frac{e^{-\mu}\mu^3}{3!}$

= $\displaystyle \frac{e^{-2\mu}{\mu^4}}{6}$

Am i right?