Show the following Maximum-Minimum Identity. For arbitrary random variables xi, i = 1, . . . , n,
max
i
xi = Σ
i
xi − Σ
20 points) Show the following Maximum-Minimum Identity. For arbitrary random variables
x_(i),i=1,dots,n,
,max_(i)x_(i)=sum_i x_(i)-sum
20 points) Show the following Maximum-Minimum Identity. For arbitrary random variables xi,i=1,...,n,
maxxi= 2
min(xi,x)+ E min(xi,xj,xk)+...+(-1)n+lmin(xi,...,xn). i<j i<j<k