Squared deviation of one variable from the sample mean

The random variables $A_1,\dots,A_{10}$ are independent, each with variance $100$, and $\mathbb{E}[A_i]=2i-1$. Let $\overline A=\tfrac1{10}\sum_{i=1}^{10}A_i$. Find $\mathbb{E}\big[(A_1-\overline A)^2\big]$.

$171$. Use second moment $=$ variance $+$ squared mean. Since $A_1-\overline A=\tfrac{9}{10}A_1-\tfrac1{10}\sum_{i\ge2}A_i$, its variance is $100\big(\tfrac{81}{100}+\tfrac{9}{100}\big)=90$. Its mean is $1-\tfrac{1}{10}\cdot100=-9$, contributing $81$. Total $171$.