(4) Suppose we use 80 hash functions to generate 80 rows in total for the signature matrix. For locality-sensitive hashing, if we split the signature matrix into 20 bands, say if columns S and S, have a similarity of 70%, what is the probability that S and S, are hashed to at least 1 common bucket? If we set the similarity threshold s = 0.7, what is the probability that S4 and S5 being similar pairs are false negatives? Element S1 0 1 1 1 2 3 4 5 6 0 0 1 0 1 S2 0 1 0 1 1 0 1 S3 0 1 1 1 0 1 1 S4 1 0 1 0 1 0 1 (1) Compute the permutations of indices of elements using the following three hash functions respectively i. h(x) = (3x + 1) mod 7 ii. h(x) = (5x + 3) mod 7 iii. h3(x) = (6x + 2) mod 7