Probability and Statistics
Category: Science > Math
Asked by: bu1234-ga
List Price: $10.00
15 Mar 2005 13:19 PST
Expires: 14 Apr 2005 14:19 PDT
Question ID: 495190
Please derive the probability density function(pdf) for a continuous Uniform Distribution
Re: Probability and Statistics
Answered By: mathtalk-ga on 15 Mar 2005 19:28 PST
Hi, bu1234-ga: To say a distribution is "uniform" means that equal size subintervals have an equal probability as "events". For a continuous distribution this means that the probability density function is a constant; it must be equal at all points of the domain, in this case all points of the interval (0,theta). Suppose the constant value of the pdf f(x) is c. We prove that c = 1/theta as a consequence of the probability measure of the entire interval being 1. That is: Pr[X in (0,theta)] = INTEGRAL f(x) dx OVER (0,theta) = INTEGRAL c dx OVER (0,theta) = c * (theta - 0) = 1 Therefore c = 1/theta is necessary. Let me know if further clarification of these points would be helpful. regards, mathtalk-ga
rated this answer:
Just as I suspected. Your verbal answer was clear and concise. thank you.
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