N
neha3
Member
A pet shop has four glass tanks in which snakes for sale are held. The shop can stock
at most four snakes at any one time because:
• if more than one snake were held in the same tank, the snakes would attempt to
eat each other and
• having snakes loose in the shop would not be popular with the neighbours
The number of snakes sold by the shop each day is a random variable with the
following distribution:
Number of Snakes Potentially Sold Probability
in Day (if stock is sufficient)
None 0.4
One 0.4
Two 0.2
If the shop has no snakes in stock at the end of a day, the owner contacts his snake
supplier to order four more snakes. The snakes are delivered the following morning
before the shop opens. The snake supplier makes a charge of C for the delivery.
(i) Write down the transition matrix for the number of snakes in stock when the
shop opens in a morning, given the number in stock when the shop opened the
previous day. [2]
(ii) Calculate the stationary distribution for the number of snakes in stock when
the shop opens, using your transition matrix in part (i). [4]
(iii) Calculate the expected long term average number of restocking orders placed
by the shop owner per trading day. [2]
CT4 S2010—7
If a customer arrives intending to purchase a snake, and there is none in stock, the sale
is lost to a rival pet shop.
Please can anyone explain me this question... I get the transaction matrix, however couldnt understand the rest of the answers...?
at most four snakes at any one time because:
• if more than one snake were held in the same tank, the snakes would attempt to
eat each other and
• having snakes loose in the shop would not be popular with the neighbours
The number of snakes sold by the shop each day is a random variable with the
following distribution:
Number of Snakes Potentially Sold Probability
in Day (if stock is sufficient)
None 0.4
One 0.4
Two 0.2
If the shop has no snakes in stock at the end of a day, the owner contacts his snake
supplier to order four more snakes. The snakes are delivered the following morning
before the shop opens. The snake supplier makes a charge of C for the delivery.
(i) Write down the transition matrix for the number of snakes in stock when the
shop opens in a morning, given the number in stock when the shop opened the
previous day. [2]
(ii) Calculate the stationary distribution for the number of snakes in stock when
the shop opens, using your transition matrix in part (i). [4]
(iii) Calculate the expected long term average number of restocking orders placed
by the shop owner per trading day. [2]
CT4 S2010—7
If a customer arrives intending to purchase a snake, and there is none in stock, the sale
is lost to a rival pet shop.
Please can anyone explain me this question... I get the transaction matrix, however couldnt understand the rest of the answers...?