Filaments used in optical fibers burn out eventually and no longer work. Suppose the working lifetimes of the filaments

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Filaments Used In Optical Fibers Burn Out Eventually And No Longer Work Suppose The Working Lifetimes Of The Filaments 1 (22.98 KiB) Viewed 42 times

Filaments used in optical fibers burn out eventually and no longer work. Suppose the working lifetimes of the filaments are distributed as exponential with mean lifetime 2.4 years. A cable for an optical fiber is composed of twelve filaments, and the cable will function properly as long as at least one filament is still working. What is the probability that the cable lasts for at least ten years? (Assume that the lifetimes of the fibers are independent.) • Define random variables Xi • Write the distribution • Write the formula for the probability explicitly • Write a R command for the probability explicitly and Round it to the nearest 4 decimal places