My home uses two light bulbs. On average, a light bulb lasts for 100 days (exponentially distributed). When a light bulb burns out, it takes an average of 10 days (exponentially distributed) before I replace the bulb. • Formulate a three-state birth-death model of this situation. • Determine the fraction of the time that both light bulbs are working. • Determine the fraction of the time that no light bulbs are working.

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My home uses two light bulbs. On average, a light bulb lasts for 100 days
(exponentially distributed). When a light bulb burns out, it takes an average of 10 days (exponentially
distributed) before I replace the bulb.
• Formulate a three-state birth-death model of this situation.
• Determine the fraction of the time that both light bulbs are working.
• Determine the fraction of the time that no light bulbs are working.
Transcribed Image Text:My home uses two light bulbs. On average, a light bulb lasts for 100 days (exponentially distributed). When a light bulb burns out, it takes an average of 10 days (exponentially distributed) before I replace the bulb. • Formulate a three-state birth-death model of this situation. • Determine the fraction of the time that both light bulbs are working. • Determine the fraction of the time that no light bulbs are working.
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