Asymptotic Performance of a System Subject to Cannibalization
Asymptotic Performance of a System Subject to Cannibalization
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In our eReader you can find the full English version of the book. Read Asymptotic Performance of a System Subject to Cannibalization Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Asymptotic Performance of a System Subject to Cannibalization
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> kx}, defined for k > and the admissible values of l, j by the equations Y, j(k) = ( 1, If X. . > kx, ij - , otherwise.
Plainly, for each Index k the random variables (Y.. (k)). _, ^ are Independent, and "^ ~ ' ' " -a. Kx 1, with probability e, . , n (1) Y. . (k) = -, 1, 1 j = l Then S. (k) denotes the number of operational parts of type 1 at time kx, given that the size of the system Is n. Setting and -a. Kx p, (k) = e ^ q^(k) = 1 - p^(k), It follows from (1) and (2) and the Independence of (...Y, . (k)). _, ^ that , n (3) -nx m/, X n-m P{S.^(k) = m} = (;;)p'!;(k)qp'(k), m = 0, 1, ... , n By definition, the system performance level at time kx Is given by the random variable $ (k) = mln S. (k) l^ln^''^^» (Y2i(k), Y22(k), ... , Y2„(k)), •••> (Y^;L^^^>^r2^^^*"-'^rn^^^^ are independent. Hence, the expected performance level at time kT can be determined from the tall distribution by the well-known formula, n-1 m) E[* (k)] = I P{* (k) > X} " x=o " n-1 = I P{S^^(k) > X, S2^(k) > X, ...
What to read after Asymptotic Performance of a System Subject to Cannibalization?
You can find similar books in the "Read Also" column, or choose other free books by Warren M Hirsch to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
> kx}, defined for k > and the admissible values of l, j by the equations Y, j(k) = ( 1, If X. . > kx, ij - , otherwise.
Plainly, for each Index k the random variables (Y.. (k)). _, ^ are Independent, and "^ ~ ' ' " -a. Kx 1, with probability e, . , n (1) Y. . (k) = -, 1, 1 j = l Then S. (k) denotes the number of operational parts of type 1 at time kx, given that the size of the system Is n. Setting and -a. Kx p, (k) = e ^ q^(k) = 1 - p^(k), It follows from (1) and (2) and the Independence of (...Y, . (k)). _, ^ that , n (3) -nx m/, X n-m P{S.^(k) = m} = (;;)p'!;(k)qp'(k), m = 0, 1, ... , n By definition, the system performance level at time kx Is given by the random variable $ (k) = mln S. (k) l^ln^''^^» (Y2i(k), Y22(k), ... , Y2„(k)), •••> (Y^;L^^^>^r2^^^*"-'^rn^^^^ are independent. Hence, the expected performance level at time kT can be determined from the tall distribution by the well-known formula, n-1 m) E[* (k)] = I P{* (k) > X} " x=o " n-1 = I P{S^^(k) > X, S2^(k) > X, ...
What to read after Asymptotic Performance of a System Subject to Cannibalization?
You can find similar books in the "Read Also" column, or choose other free books by Warren M Hirsch to read onlineMoreLess
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