Tom the cat patrols the house in search of the mouse Jerry, who wants to get into the kitchen for something to eat. After leaving the kitchen, Tom will return after a random amount of time, which follows an exponential distribution with mean 15 seconds. Assume also that Jerry waited for 5 seconds without seeing Tom returning to the kitchen before starting to cross the house. Suppose Jerry needs 10 seconds to get across the house, and starts immediately after Tom leaves the kitchen. What is the probability that Jerry the mouse will get caught by Tom the cat?
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!
Tom the cat patrols the house in search of the mouse Jerry, who wants to get into the kitchen for something to eat.
After leaving the kitchen, Tom will return after a random amount of time, which follows an exponential distribution with mean 15 seconds.
Assume also that Jerry waited for 5 seconds without seeing Tom returning to the kitchen before starting to cross the house.
Suppose Jerry needs 10 seconds to get across the house, and starts immediately after Tom leaves the kitchen. What is the probability that Jerry the mouse will get caught by Tom the cat?
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