Covariance between the first elements of the samples There are two non-independent samples $a_1, a_2, ... ,a_n$ and $b_1, b_2, ..., b_n$.
In Python I can calculate with np.cov($\{a_1, ..., a_n\},\{b_1, ..., b_n\}$ ) сovariance between these samples.
But how can I get $cov (a_1, b_1)$? Both samples are generated from some known distribution.
This question is probably not very difficult, but I don't specialize in statistics, so I will be grateful for the help!

Without variance in your sample there is no covariance.
Think of the sample covariance formula:
$$
cov (A, B) = \frac{1}{n} \sum_{i=1}^n (a_i - \bar{a})(b_i - \bar{b})
$$
For only one observation, the observations $a_i$ and $b_i$ would be equal to their sample means $\bar{a}$ and $\bar{b}$ and the result would be zero.
