Consider two machines that are maintained by a single repairman. machine i functions for an exponentially distributed amount of time with rate λi before it fails. the repair times for each unit are exponential with rate μi. they are repaired in the order in which they fail. formulate a markov chain model for this situation with state space {0, 1, 2, 12, 21}. (b) suppose that λ1 = 1, μ1 = 2, λ2 = 3, μ2 = 4. find the stationary distribution.

For every corresponding pair of cross sections, the area of the cross section of a sphere with radius r is equal to the area of the cross section of a cylinder with radius and height 2r minus the volume of two cones, each with a radius and height of r. a cross section of the sphere is and a cross section of the cylinder minus the cones, taken parallel to the base of cylinder, is the volume of the cylinder with radius r and height 2r is and the volume of each cone with radius r and height r is 1/3 pie r^3. so the volume of the cylinder minus the two cones is therefore, the volume of the cylinder is 4/3pie r^3 by cavalieri's principle. (fill in options are: r/2- r- 2r- an annulus- a circle -1/3pier^3- 2/3pier^3- 4/3pier^3- 5/3pier^3- 2pier^3- 4pier^3)