ii) (6 points) Recall that for random variables X and Y with respective standard devi- ations ox and oy, their Pearson's correlation coefficient is given by corr(X, Y) _ COV (X , Y ) OXOY Also recall that the cosine similarity between two vectors u, v is the cosine of the angle 6 between them, and is related to the inner product as follows: (u, v) cos 6 = lullvl Show that for two vectors u, v E R" with zero elementwise mean, the correlation between their elements is equal to their cosine similarity