# continuos uniform distribution pdf value at upper bound

What is the most formal (and coerent with probability theory) definition for the value of pdf(b) where b is the upper bound of the support of the continuos uniform distribution U(a,b) ? We can choice:

• pdf(b) = 1/(b-a)
• pdf(b) = 0
• pdf(b) = undefined
• The first one. It's a uniform distribution, so the value is constant across its interval. – Adrian Keister Jul 15 at 19:10
• @AdrianKeister in any of these cases is a continuos uniform distribution. – frhack Jul 15 at 20:06
• No pdf is defined, as a function, at any point. As a convention, a pdf is often represented as a function that is continuous wherever possible. Because no pdf for this distribution can be continuous at either endpoint, it cannot be uniquely defined at either endpoint according to such a convention. In this sense the last bullet is rigorously the answer, but the other two bullets are perfectly valid, too. – whuber Jul 15 at 20:26
• @whuber look here probabilitycourse.com/chapter4/4_1_1_pdf.php – frhack Jul 15 at 20:38
• if we define PDF as derivative of the CDF then the PDF is not defined in a, b – frhack Jul 15 at 20:51