Atotal of m white and m black balls are distributed among two urns, with each urn containing m balls. at each stage, a ball is randomly selected from each urn and the two selected balls are interchanged. let xn denote the number of black balls in urn 1 after the nth interchange.

(a) give the transition probabilities of the markov chain xn, n 0.
(b) without any computations, what do you think are the limiting probabilities of this chain?
(c) find the limiting probabilities and show that the stationary chain is time reversible.

Julius sold five times as many computers as sam sold last year. in total, they sold 78 computers. how many computers did julius sell?

The school track has eight lanes. each lane is 1.25 meters wide. the arc at each end of the track is 180. the distance of the home straight and the radii for the arcs in the 1st 4 lanes are given. s=85m r1=36.5m r2=37.75m r3=39m r4=40.25m part one: find the radii of lanes 5 through 8 of the track. show your work. part two: if max ran around lane one, how far did he run? show your work and explain your solution. part three: max wants to run a total of three laps around the track, choose two additional lanes (2-8) for him to run and find the distance around those two lanes. show your work and round to the hundredths. part 4: based on your lane choices in part three, what was the total distance max ran in the three laps around the track?

Parallelogram efgh is a rectangle. he = 6, and fe = 8. find ge: and find fj: