Let X1,...„Xn and Y2,...,Yn be independent random vectors, with each vector being a random...

Let X1,...„Xn and Y2,...,Yn be independent random vectors, with each vector being a random ordering of k ones and n — k zeros. That is, their joint probability mass functions are

Let

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 Xi  = 1, Yi= 0.

(a) Relate N to M.

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(b) What is the distribution of M

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(c) Find E[N].

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(d) Find Var(N).