Some functions drawn from different Gaussian processes are depicted as below:
We know that for all of the processes, the mean is equal to zero.
We are also given 5 covariance matrices, and we are told that each covariance corresponds to exactly one of those processes. The question is:
Match the processes with the covariances:
(1) $Cov(y_{i_1}, y_{i_2})= x_{i_1}x_{i_2}$
(2) $Cov(y_{i_1}, y_{i_2})= 5^2+5^2x_{i_1}x_{i_2}+0.5^2 \exp(-((x_{i_1}-x_{i_2})/0.1)^2)$
(3) $Cov(y_{i_1}, y_{i_2})= 0.5^2\exp(-((x_{i_1}-x_{i_2})/0.5)^2)$
(4) $Cov(y_{i_1}, y_{i_2})= 8^2\exp(-((x_{i_1}-x_{i_2})/5)^2)$
(5) $Cov(y_{i_1}, y_{i_2})= 0.7^2\exp(-((x_{i_1}-x_{i_2})/0.1)^2)+8^2\exp(-((x_{i_1}-x_{i_2})/2)^2)$
Note: I know that the result is: (d)->3, (a)->1, (e)->2, (b)->5, (c)->4
I have used python libraries (sklearn) to depict the processes (and this is how I know the answer). However, I want to know if there is a better way to solve this mathematically (and without using programming skills).