Talk:Probability mass function

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Including a Citation

I was about to "correct" the half-closed interval in the first paragraph. Is there a good way to link this to article on Intervals? --Adolphe Youssef (talk) 18:10, 13 March 2008 (UTC)[reply]

I added a wikilink to handle this. Melcombe (talk) 16:48, 4 August 2008 (UTC)[reply]

Specific formulation as a function?

What is the definition of the funcrion to be? At present it is in the form f(x) where x is essentially continuous. The reference I added use the form f(j) where j is an integer which indexes the support points of the distribution. Possibly we need both. Melcombe (talk) 16:51, 4 August 2008 (UTC)[reply]

PMF may fail to be diffable even when it vanishes

Let f_X be defined as: f_X(x) = x/2, for x = 1, 1/2, 1/4, 1/8, 1/16, ...; and f(x) = 0 otherwise. Then X never takes on the value 0, yet f_X is not differentiable at 0. 207.62.177.227 (talk) 18:19, 20 November 2008 (UTC)[reply]

Open Interval

Why not just use a closed interval for pdf?

My guess is that the author was either thinking of (a) expressing the integral in terms of the cumulative distribution function: P(a < X ≤ b) = F_X(b) − F_X(a); or (b) the fact the semi-infinite-closed intervals (− ∞, x] are often used to generate the Borel sigma-algebra on the reals. 75.95.125.245 (talk) 05:47, 24 November 2008 (UTC)[reply]