Chapter 6, Problem 6.18STPE

6.18. Let

4V’H and

Y, be independent random vectors, with each vector being a random ordering of k ones and ii — I zeros. That is, their joint probability mass functions are

= i1.. . ., .X’,, = i,1} = P{)1 = i1.. . .. = i,1}

1

= ,ij=o,1, j=1ij=:1I.

(n

\

N = 1=1Ix—)’;

I denote the number of coordinates at which the two vectors have different values. Also, let

M denote the number of values of i for which

= 0.

a. Relate N to M.

b. What is the distribution of M?

c. Find E [ N].

d. Find Var (N).