Why do we use $\lambda$ as a symbol for expected value at Poisson distribution instead of $\mu$?

Question

Is there a reason why we call it differently?

Answer 1

The $\lambda$ possibly comes as the rate parameter of a Poisson process, so the expected number of events per unit time is $\lambda$ while the expected gap between events is $\frac1\lambda$

Using $\mu$ instead might slightly aid understanding for the former (a Poisson distribution), but would probably lead to greater confusion for the latter (an exponential distribution)

Answer 2

My convention, $\mu$ is used to denote means/expected value, and $\lambda$ is often used to denote rate parameters.

For a Poisson distribution, the rate parameter is the mean/expected value. Hence you will find that both $\mu$ and $\lambda$ are often used to denote the distribution parameter.

$\lambda$ may be more common, but both are used.