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Suppose n = 2^k, and let v = (v_1,...,v_k+1) be a uniform random vector in {0,1}^k+1. For each integer i in {0,1,...,n-1}, let b_i= (i_1, i_2, ..., i_k, 1) be the binary expansion of i with a 1 appended. Define Y_i = b_i * v (dot product). Show that the Y_i are 3-wise independent.