13. This problem might require thought. A lamp holds 3 bulbs. There are two kinds of bulbs, short-lived red ones with me

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13 This Problem Might Require Thought A Lamp Holds 3 Bulbs There Are Two Kinds Of Bulbs Short Lived Red Ones With Me 1 (94.69 KiB) Viewed 146 times

13. This problem might require thought. A lamp holds 3 bulbs. There are two kinds of bulbs, short-lived red ones with mean lifetime 1 day, and long-lived green ones with mean lifetime 3 days. All bulb lifetimes have exponential distributions independent of each other. Whenever a green light bulb burns out, it is replaced by a red one. Whenever a red light bulb burns out, it is replaced by a green one. Define variables and write equations that, if solved, would yield the probability distribution of the number of green light bulbs at a random moment when a bulb has just been replaced.