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The probability density function of an exponentially distributed random variable with mean 1/λ is λ e-At for t > 0. Suppose the lifetime of a particular brand of light bulb follows an exponential distribution with a mean of 1000 hours. If a light fixture is equipped with two such bulbs, then what is the probability that it still illuminates a room after 1000 hours? Develop your answer by evaluating a double integral. What assumption must you make about the respective lifetimes of the bulbs?Make sure to use double integral formula since the question asks for it. Thanks

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