Probability function (p.f) of a random variable

[serbskak]

If one has a Bernoulli random variable W that is derived from a Variable T (Poisson λ), by the following rules W = (if T=0 then W=1 and if T>0 then W=0), I am having trouble finding the pf for W. Any suggestions about how to proceed forward?

 

[Evgeny.Makarov]

Welcome to the forum.

The distribution for $T$ says that $P(T=0)=\frac{\lambda^0}{0!}e^{-\lambda}$. By assumption $P(W=1)=P(T=0)$ and $P(W=0)=1-P(T=0)$.