Question

A study conducted by the Urban Energy Commission in a large metropolitan area indicates the probabilities that homeowners within the area will use certain heating fuels or solar energy during the next 10 years as the major source of heat for their homes. The transition matrix representing the transition probabilities from one state to another is

(transition matrix)	Elec.	gas	oil	solar
Electricity	.70	0	0	0
gas	.15	.90	.20	.05
oil	.05	.02	.75	0
solar	.10	.08	.05	.95

Among homeowners within the area, 15% currently use electricity, 35% use natural gas, 40% use oil, and 10% use solar energy as the major source of heat for their homes. What is the expected distribution of the homeowners that will be using each type of heating fuel or solar energy within the next decade? (Round your answers to two decimal places.)

Answer 1