=+26. Consider the n-dimensional unit cube [0, 1]n. Suppose that each of its n2n−1 edges is independently assigned one of two equally likely orientations. Let S be the number of vertices at which all neighboring edges point toward the vertex. Show that S has mean E(S)=1 and variance Var(S)=1 − (n + 1)2−n. When n is large, S follows an approximate Poisson distribution. (Hint: Let Xα be the indicator that vertex α has all of its edges directed toward α. Note that Xα is independent of Xβ unless α and β share an edge. If α and β share an edge, then XαXβ = 0.)