The table below shows the time intervals, in seconds, between successive white cars in free flowing traffic on an open road. Can these times be modeled by an exponential distribution? Use 5% level of significance. Time 0---20 20---40 40---60 60---90 90---120 120---180 Observed Frequency 41 19 16 13 9 2 Expected frequency 39.3 23.9 14.5 11.8 5.5 5 Note: Here 1 parameter estimate
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!
The table below shows the time intervals, in seconds, between successive white cars in free flowing traffic on an open
road. Can these times be modeled by an exponential distribution? Use 5% level of significance.
Time 0---20 20---40 40---60 60---90 90---120 120---180
Observed Frequency 41 19 16 13 9 2
Expected frequency 39.3 23.9 14.5 11.8 5.5 5
Note: Here 1 parameter estimate
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