UK Sep'13 Q.8) three parking spaces

[deepakraomore]

There are 3 parking places outside apartment.
Prob. That car seeking parking in short time dt. Adt+o(dt)
Prob owner drives away in short time dt is
Bdt+o(dt)
State space {0,1,2,3} transitions are from 0 to 1 to 2 to 3 and vice versa
Then how the rate from 0 to 1 is 3B,
from 1 to 2 is 2B

 

[BrianCunningham]

From state 0 to 1, any of the three cars that are parked there can drive away, so the transition rate from 0 to 1 (or from three cars parked to two cars parked) is the sum of the transition rates of any of the three cars moving away; i.e 3 * B. Similar logic applies for the transition from 1 to 2 etc.

 

[deepakraomore]

Thanks a million