A lamp has two bulbs of a type with an average lifetime of 1000 hours. Assuming that we can model the probability of failure of these bulbs by an exponential density function with mean ? = 1000, find the probability that both of the lamp’s bulbs fail within 1000 hours. (b)Another lamp has just one bulb of the same type as in part (a). If one bulb burns out and is replaced by a bulb of the same type, find the probability that the two bulbs fail within a total of 1000 hours.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A lamp has two bulbs of a type with an average lifetime of 1000 hours.
Assuming that we can model the probability of failure of these bulbs by
an exponential density
that both of the lamp’s bulbs fail within 1000 hours.
(b)Another lamp has just one bulb of the same type as in part (a). If one bulb
burns out and is replaced by a bulb of the same type, find the probability
that the two bulbs fail within a total of 1000 hours.
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