Showing papers by "Indian Institute of Management Calcutta published in 1969"
TL;DR: In this paper, the authors define the events A, B and C as follows: A: Xr_1,n-1? X < Xr+l,n, Yk,n < Yr,n −1 ; B: X r,n,n < X r,n − 1 ; C: X n,n.
Abstract: 2. THE RECURRENCE RELATION r n n-i n-i Theoremi: AiGr k(X, y) = FI(x)A/GlG,k(x, y) F(x, Y)Al,2Gr_-,k-l(X, Y), n (2 2). Proof: Let us define the events A, B and C as follows: A: Xr_1,n-1 ? X < Xr,n-11 Yk,n-1 < Y; B: Xr-l,n-1 < X < Xr,n-1, Yk-1,n-1 < Y < Yk,n-1; C: Xr,n < X < Xr+l,n, Yk,n < Y Then we observe that n-i (4) P(A) = A/Grl,k(X, Y), P(B) ~n-i P(B) = A1,2Gr-1,k-1(X, ), (5) P(C) = AiGr,k(X, Y). (6) 600
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