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- The life times, YY in years of a certain brand of low-grade lightbulbs follow an exponential distribution with a mean of 0.5 years. A tester makes random observations of the life times of this particular brand of lightbulbs and records them one by one as either a success if the life time exceeds 1 year, or as a failure otherwise. Find the probability to 3 decimal places that the first success occurs in the fifth observation.The failure rate of an electronic system is 0.005 failures per hour and its timeto failure can be modelled by an exponential distribution.Calculate the probability that the system will fail 50 hours mission.The length of time that a student takes to complete her homework is uniformly distributed between 3 and 5 hours.Find the probability that she completes her homework in less than 190 minutes.