Hi please use the given information to answer each part of the problem and please include a short explanation, drawing, or steps/formulas to improve my understanding of the problem. Thank you!

The sample space 9 of an experiment consists of all 8 dimensional binary vectors, e.g., every member of Q has the form a: = (we, . . . ,w7), Where wi is 0 or 1. The probability law P assigns a probability of 1/28 to each of the 28 elements in 9. Find the 13me describing the following random variables: (a) W(w) = 237:0 wi, i.e., the number of 1's in the binary vector. (b) Z(w) = mane-(ma)