The time (in hours) required to repair a machine is an exponential distributed random variable with parameter λ = 1 2 . a) What is the probability that a repair time exceeds 4 hours? b) What is the probability that a repair time takes at most 3 hours? c) What is the probability that a repair time takes between 2 to 4 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!
The time (in hours) required to repair a machine is an exponential distributed random variable
with parameter λ =
1
2
.
a) What is the
b) What is the probability that a repair time takes at most 3 hours?
c) What is the probability that a repair time takes between 2 to 4 hours?
d) What is the median repair time of the machine?
e) What is the conditional probability that a repair takes at least 10 hours, given that its
duration exceeds 9 hours?
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