FREQUENTLY ASKED QUESTIONS FOR HOMEWORK 5

1.  PROBLEM 12.4(a): how do we find the probabilities
    when setting up a transition matrix?  Is it correct to assume that we
    are going from the end of one week to the beginning of the next week? 
    (Or is it to the end of the next week)?

ANSWER: The current stage is at the end of this week before you've decided
whether or not to place an order.  The next stage is the end of next week
(again before you've decided to place an order.)

You need to use the Poisson distribution to compute the probabilities.
For example, P(0 end of next week | 0 end of this week) means you placed
an order of size 3 and all 3 units were bought during the week.  It means
that there was a demand for 3 OR MORE units (why not just 3??)

So  P(0 end of next week | 0 end of this week) = P(X >= 3) where X is the
random variable for demand.  X follows a Poisson distribution.  Your text
discusses the Poisson distribution -- check the index for the page with
the formula.

The process of building the transition matrix is lengthy but
straightforward.

2.  PROBLEM 12.12(a):  how do we find the probabilities
    when setting up a transition matrix?

ANSWER: Here there are 9 different states and each state has 2
attributes: the number sold yesterday and the number sold the 
day before yesterday.  So the CURRENT STAGE (today) looks at
(yesterday, day before yesterday) while the NEXT STAGE (tomorrow)
looks at (today, yesterday).

Having said that, it's a matter of putting the given probabilities
into the correct cell of your 9x9 transition matrix.

3.  PROBLEM 12.9: Could you help me get started on this one?

ANSWER: Your tansition matrix is already provided.  For part (a)
you need the state vector for stage 4.  For part (b) you need
the probability that movies 2 and 3 are turkeys given that 
movie 1 was a blockbuster.  (So look at the next 2 stages).
For part (c) you want to check whether or not the star retires
during the next 2 stages.