1. Given the set $M=\{1,2, \cdots, 2020\}$, for any non-empty subset $A$ of $M$, $\lambda_{A}$ is the sum of the largest and smallest numbers in the set $A$. Then the arithmetic mean of all such $\lambda_{A}$ is $\qquad$
Reference answer: Consider the subset $A^{\prime}=\{2021-x \mid x \in A\}$ of $M$. If $A^{\prime}=A$, then $\lambda_{A^{\prime}}=\lambda_{A}=2021$. If $A^{\prime} \neq A$, let the maximum number in $A$ be $a$, and the minimum number be $b$, then the maximum number in $A^{\prime}$ is $2021-b$, and the minimum number is $2021-a$, at this time, $\frac{\lambda_{A}+\lambda_{A}}{2}=2021$. Therefore, the required arithmetic mean is 2021.