Question $1.(8$ points$)$

$($a$)$ For binary data, the L$1$ distance corresponds to the Hamming distance; that is$,$ the number of bits that are different between two binary vectors. The Jaccard similarity is a measure of the similarity between two binary vectors. Compute the Hamming distance and the Jaccard similarity between the following two binary vectors.

$x=0101010001$

$y=0000011001$