sensor connected to a control center indicates that there is damage somewhere along a particular 4-mile length of train track. The conductor thinks that the exact location of the damage is uniformly distributed between mile 0 and mile 4 of that length of track. Let X be the distance along the track from mile 0 to the location of the damage. a) What is the expected value of X? b) What is the probability that the damage is located between mile 2 and mile 4 of that length of track? c) Suppose the interval of track between miles 0 and 1 is checked carefully, and no damage is found. Given this, what is the probability that the damage is located betwee
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 sensor connected to a control center indicates that there is damage somewhere along a particular 4-mile length of train track.
The conductor thinks that the exact location of the damage is uniformly distributed between mile 0 and mile 4 of that length of track. Let X be the distance along the track from mile 0 to the location of the damage.
a) What is the expected value of X?
b) What is the probability that the damage is located between mile 2 and mile 4 of that length of track?
c) Suppose the interval of track between miles 0 and 1 is checked carefully, and no damage is found. Given this, what is the probability that the damage is located between miles 2 and 4?
Given that X follows uniform distribution with minimum value 0 and maximum value 4.
a)
Expected value of X:
b)
The probability that the damage is located between mile 2 and mile 4 of that length of track is,
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