medium Probability
A release-checked medium problem for training Covariance, Expected Value.
Suppose that $A_1, \dots, A_{10}$ are independent random variables such that $\mu_i = \mathbb{E}[A_i] = 2i-1$ and $\text{Var}(A_i) = 100$ meaning there is a common variance $100$ but not a common mean. Define $\overline{\mu} = \dfrac{1}{10}\displaystyle \sum_{i=1}^{10} \mu_i$. Compute $\mathbb{E}[(A_1 - \overline{A})^2]$.
This Probability problem is tagged Covariance, Expected Value. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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