Exponential Distribution (p108)
- Thread starter ajsa
- Start date
Hi ajsa,
1) total area under pdf curve = 1. But y = f(x) can indeed be greater than one, and is for several distributions; b/c there is no probability such that p() = f(x) under continous. Continuous (PDF) needs an interval, so probability p(x) does not equal f(x) rather the probability = *area* carved out by interval: p(x) = f(x) * width of interval, approximately. (thus starts integrals)
In short, probabilty must < 1, but f(x) is not probability
2) Yes, in our application of Exp() which uses it to model "waiting times," x is time. You might like this learning XLS: http://www.bionicturtle.com/premium/spreadsheet/2.c.2._poisson_vs._exp/
....if you look into this, you'll note the "time dimension" is built-into the lambda. I have lambda = 6 events per day, which is then translated into (equates to) an average of 0.25 events per hour; i.e., 6/24 hours = 1 event / 0.25 hours, reciprical = 0.25 events/hour. Such that my "X" as used is hours, but could be another time unit.
David
1) total area under pdf curve = 1. But y = f(x) can indeed be greater than one, and is for several distributions; b/c there is no probability such that p() = f(x) under continous. Continuous (PDF) needs an interval, so probability p(x) does not equal f(x) rather the probability = *area* carved out by interval: p(x) = f(x) * width of interval, approximately. (thus starts integrals)
In short, probabilty must < 1, but f(x) is not probability
2) Yes, in our application of Exp() which uses it to model "waiting times," x is time. You might like this learning XLS: http://www.bionicturtle.com/premium/spreadsheet/2.c.2._poisson_vs._exp/
....if you look into this, you'll note the "time dimension" is built-into the lambda. I have lambda = 6 events per day, which is then translated into (equates to) an average of 0.25 events per hour; i.e., 6/24 hours = 1 event / 0.25 hours, reciprical = 0.25 events/hour. Such that my "X" as used is hours, but could be another time unit.
David
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