easy Probability
A release-checked easy problem for training Covariance/Correlation, Uniform, Geometric Probability.
$n$ independent points $P_i = (X_i,Y_i)$ are selected uniformly at random from the boundary of the unit circle. Define $\overline{X} = \displaystyle \dfrac{1}{n}\sum_{i=1}^n X_i$ and $\overline{Y} = \displaystyle \dfrac{1}{n}\sum_{i=1}^n Y_i$. Compute $\cov{\overline{X}}{\overline{Y}}$ when $n = 10$.
This Probability problem is tagged Covariance/Correlation, Uniform, Geometric Probability. 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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