If a company pays a quarterly dividend,the next is paid with probability .7. If it stops a dividend,the next is not paid with probability .5. Find the long-run probability of not paying,to three decimals.
Let π be the stationary not-paid probability. Balance gives π=.3(1−π)+.5π,so .8π=.3 and π=**0.375**. Both transitions permit an irreducible aperiodic two-state chain,so this stationary probability is the long-run limit.
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