Give a True or False answer and a short explanation.

a$.$ For binary vectors, mutual information is more similar to correlation than the Jaccard

measure.

b$.$ The Jaccard coefficient for two binary strings $($i$.$e$.,$ strings of $0$s and $1$s$)$ is always greater

than or equal to the cosine similarity for the two binary strings. $($Hint: try different

cases.$)$

c$.$ For reducing the size of a daily time series, it would be better to sample than aggregate

since sampling is a simpler process. Explain.