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What is the value of $\lambda$ such that $\operatorname{Prob}\{X>\operatorname{mean}\{X\}\}=1 / e$, where $\text{PDF}$ of $X$ is $p_{X}(x)=\lambda e^{-\lambda x}, x \geq 0, \lambda>0?$ 

  1. $1$
  2. $1 / e$
  3. $1 / \sqrt{e}$
  4. $1 / e^{2}$
  5. All of the above
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