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Largest $M-1$ RV

The expressions simplify considerably when we seek the largest $M-1$ RV. Thus, $t_i = i, \; 1\leq i \leq M-1$. We have

$\displaystyle D\stackrel{\mbox{\tiny$\Delta$}}{=}(N-M+1)!, $

and

$\displaystyle I(\lambda) \stackrel{\mbox{\tiny$\Delta$}}{=}c(z_{M-1},\lambda)^{N-M+1} $