FIVE- M IN U T E A N A LYST
Markov’s nursery
Because there are
two children, there are
a total of four states that
the children could
be in: 1. both sleeping; 2.
Mary only sleeping;
3. Neil only sleeping; and
4. both crying.
BY HARRISON
SCHRAMM, CAP
72
|
This month, we tackle a problem that may be
familiar to some readers – the issue of getting
multiple young children to sleep. We’ll also use
this column to (re)introduce some neat mechanics
– the generator matrix. Suppose that a family has
two infant children, named Mary and Neil. Now, at
bedtime, for analytic purposes, they exist in one
of two states: “crying” or “sleeping” [1]. Because
there are two children, there are a total of four
states that the children could be in: 1. both sleeping; 2. Mary only sleeping; 3. Neil only sleeping;
and 4. both crying.
We would like to know the amount of time the system (nursery) spends in each state, particularly the
proportion of time both children are asleep. There’s
a minor twist to this problem – we assume that if one
child is crying, it will reduce the amount of time that
the other child is sleeping by half if they are sleeping,
or lengthen the amount of time that the other child
stays awake if they are currently awake.
A N A LY T I C S - M A G A Z I N E . O R G
W W W. I N F O R M S . O R G