Let X = the time between two successive arrivals at the drive-up window of a localbank. If X has an exponential distribution with λ = 1 (which is identical to a standardgamma distribution with α = 1), compute the following:a. The expected time between two successive arrivalsb. The standard deviation of the time between successive arrivalsc. P(X ≤ 4) d. P(2 ≤ X ≤ 5)
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!
Let X = the time between two successive arrivals at the drive-up window of a local
bank. If X has an exponential distribution with λ = 1 (which is identical to a standard
gamma distribution with α = 1), compute the following:
a. The expected time between two successive arrivals
b. The standard deviation of the time between successive arrivals
c. P(X ≤ 4) d. P(2 ≤ X ≤ 5)
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