At a train station, the time between trains leaving the station follows an Exponential distribution with parameter λ = 1/15 minutes. (a) You arrive at the train station at 12:30pm right as the train pulls out of the station and you miss this train. What is the probability the next train leaves after 12:50pm? (b) What is the expected waiting time between trains leaving the station?
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!
At a train station, the time between trains leaving the station follows an Exponential distribution with parameter λ = 1/15 minutes.
(a) You arrive at the train station at 12:30pm right as the train pulls out of the station and you miss this train. What is the
(b) What is the expected waiting time between trains leaving the station?
The probability distribution function of exponential distribution is given by , where parameter is given and it is .
And the cumulative distribution function of exponential distribution is given by .
Here it is given that time between trains is following exponential distribution and last train departed at 12:30 pm. It is asked to find the probability that next train departs after 12:50 pm means the time between two trains is more than 20 minutes.
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