A sequence y1,y2,…,yk of real numbers is called <spanclass=′latex−italic′>zigzag</span> if k=1, or if y2−y1,y3−y2,…,yk−yk−1 are nonzero and alternate in sign. Let X1,X2,…,Xn be chosen independently from the uniform distribution on [0,1]. Let a(X1,X2,…,Xn) be the largest value of k for which there exists an increasing sequence of integers i1,i2,…,ik such that Xi1,Xi2,…Xik is zigzag. Find the expected value of a(X1,X2,…,Xn) for n≥2.