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A Poisson random variable $X$ is given by $\operatorname{Pr}\{X=k\}=\mathrm{e}^{-\lambda} \lambda^{k} / k !, k=0,1,2, \ldots$ for $\lambda>0$. The variance of $X$ scales as

  1. $\lambda$
  2. $\lambda^{2}$
  3. $\lambda^{3}$
  4. $\sqrt{\lambda}$
  5. None of the above
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