A guard patrols a museum in order to catch possible thieves. After leaving the entrance, the guard will return after a random amount of time, which follows an exponential distribution with a mean of 15 minutes. Assume the time needed for a thief to break in is an exponential random variable with a mean of 10 minutes. If the thief starts to break in immediately after the guard leaves the entrance, what is the probability that the thief will get caught?
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 guard patrols a museum in order to catch possible thieves. After leaving
the entrance, the guard will return after a random amount of time, which follows an exponential distribution with a
Assume the time needed for a thief to break in is an exponential random variable with a mean of 10 minutes.
If the thief starts to break in immediately after the guard leaves the entrance, what is the
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