. A fair die is rolled repeatedly. Let X denote the largest number shown up after the n-th roll, n = 1, 2, .... a) Determine the transition probability matrix. ( c) Find the limiting probabilities for each state.
. A fair die is rolled repeatedly. Let X denote the largest number shown up after the n-th roll, n = 1, 2, .... a) Determine the transition probability matrix. ( c) Find the limiting probabilities for each state.
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![6
A fair die is rolled repeatedly. Let X denote the largest number shown up after the n-th roll, n = 1, 2, … … ….
a) Determine the transition probability matrix.
c) Find the limiting probabilities for each state.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d3e9328-f26c-468d-a75c-4c46a9fae1af%2Fa9014eee-5346-4904-9af9-2e72bad711f9%2Fcjj1su_processed.png&w=3840&q=75)
Transcribed Image Text:6
A fair die is rolled repeatedly. Let X denote the largest number shown up after the n-th roll, n = 1, 2, … … ….
a) Determine the transition probability matrix.
c) Find the limiting probabilities for each state.
![.
A single product inventory system with a storage capacity of 2 units is replenished weekly using the following
policy: if there are 0 or 1 units in stock, order up to the storage capacity; else, do not order. Weekly demands
are iid rv's with pmf P(D = k) = 0.1+ 0.1k, k = 0, 1, 2, 3. Any unmet demand is lost. Assume zero order re-
plenishment time. For any week, the ordering cost is 3n, where n is the number of units ordered during the week.
The weekly storage cost is 1.5m, where m is the number of units on hand at the beginning of the week (before ordering).
a) Calculate the long-run expected average total cost (LREAC) of ordering and storage for this policy. (
b) An alternative ordering policy is considered: if there are zero units in stock, order 2 units; else, do not order.
Compare this policy to the original one on the basis of LREAC. (](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d3e9328-f26c-468d-a75c-4c46a9fae1af%2Fa9014eee-5346-4904-9af9-2e72bad711f9%2Fbnc3duf_processed.png&w=3840&q=75)
Transcribed Image Text:.
A single product inventory system with a storage capacity of 2 units is replenished weekly using the following
policy: if there are 0 or 1 units in stock, order up to the storage capacity; else, do not order. Weekly demands
are iid rv's with pmf P(D = k) = 0.1+ 0.1k, k = 0, 1, 2, 3. Any unmet demand is lost. Assume zero order re-
plenishment time. For any week, the ordering cost is 3n, where n is the number of units ordered during the week.
The weekly storage cost is 1.5m, where m is the number of units on hand at the beginning of the week (before ordering).
a) Calculate the long-run expected average total cost (LREAC) of ordering and storage for this policy. (
b) An alternative ordering policy is considered: if there are zero units in stock, order 2 units; else, do not order.
Compare this policy to the original one on the basis of LREAC. (
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