The number of workplace injuries, $N$, occuring in a factory on any given day is Poisson distributed with mean $\lambda$ . The parameter $\lambda$ is a random variable that is determined by the level of activity in the factory, and is uniformly distributed on the interval $[0,3]$. Calculate $Var[N]$.
The answer 2.25 and i saw the answer used the relationship of $Var[N]=E(Var(N|\lambda)+Var(E[N|\lambda])$ but I'm not sure why this conditional probability is needed to be applied. Hope someone can explain how I should approach this problem thanks!