Consider the inventory example below Xt = number of cameras on hand at the end of week t Start with one camera in stock, that is Xo = 1 If Xt = 0, order 2 cameras If Xt > 0, do not order any cameras 0.5 0.251 0 0.25 L0.25 0.5 0.25 (a) Find the Mij (the expected first passage time from state i to state j) for all i and j. (b) Find the expected time until the first order is submitted. (c) Find the expected time between orders. [0.25 The transition matrix for this Markov chain is P = 0.75

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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4. Consider the inventory example below
Xt
Start with one camera in stock, that is Xo
If Xt
0, order 2 cameras
If Xt > 0, do not order any cameras
number of cameras on hand at the end of week t
=
=
1
[0.25
0.5
0.75 0.25
L0.25 0.5
(a) Find the Mij (the expected first passage time from state i to state j) for all i and j.
(b) Find the expected time until the first order is submitted.
(c) Find the expected time between orders.
0.251
0
0.25]
The transition matrix for this Markov chain is P
=
Transcribed Image Text:4. Consider the inventory example below Xt Start with one camera in stock, that is Xo If Xt 0, order 2 cameras If Xt > 0, do not order any cameras number of cameras on hand at the end of week t = = 1 [0.25 0.5 0.75 0.25 L0.25 0.5 (a) Find the Mij (the expected first passage time from state i to state j) for all i and j. (b) Find the expected time until the first order is submitted. (c) Find the expected time between orders. 0.251 0 0.25] The transition matrix for this Markov chain is P =
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