2. Binary vectors. (10 points) The sample Space [2 of an experiment consists of all 8- dimensional binary vectors, e.g., every member of Q has the form w = (010,. ..,w7), Where wz- is 0 or 1. The probability law P assigns a probability of 1/28 to each of the 23 elements in 9. Find the pmfs describing the following random variables: (a) W(w) = 23:0 w,\" i.e., the number of 1's in the binary vector. (b) Z (w) = maxi-(mi)