Regarding a question, where the lifespan of a machine part is exponentially distributed with $\lambda=1/10$. When asked about the average lifespan of $100$ independent components, why is $\mathbb{E}(X)=10$ and $SD(X)=\frac{10}{\sqrt{100}}$? Can someone explain how one arrives at the standard deviation, and why its not equal to $\mathbb{E}(X)$, or why we don't use the Gamma Distribution (where $\mathbb{E}(X)=\frac{r}{\lambda}$ and $SD(X) =\frac{\sqrt{r}}{\lambda}$ respectively in this case? Am I misunderstanding the problem conceptually?
E(X) and Standard Deviation of Independent Exponential Distributions
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probability