

Subject:
Probability and Statistics
Category: Science > Math Asked by: bu1234ga List Price: $10.00 
Posted:
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  
 


Subject:
Re: Probability and Statistics
Answered By: mathtalkga on 15 Mar 2005 19:28 PST Rated: 
Hi, bu1234ga: 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, mathtalkga 
bu1234ga
rated this answer:
Just as I suspected. Your verbal answer was clear and concise. thank you. 

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