Plants grow naturally towards the strongest source of light, this is called phototropism. They do this in order to maximise their exposure to the sun and increase the amount of photosysnthesis (and therefore growth). This is a survival mechansim.
researcher will either use random assignment or matching What do random assignment and matching have in common? They are both designed to create equivalent groups of participants. Random assignment is to random selection as _____ is to _____
It occurs to me that even the requirement for identical distribution of the $X_i$ is not needed to prove that the random walk is not covariance stationary. Independence and nonzero variance (or at least one $X_i$ having nonzero variance) might suffice.