http://www.bing.com:80/search?q=Continuous+Probability+Distribution+ChartSearch resultshttp://www.bing.com:80/s/a/rsslogo.gifhttp://www.bing.com:80/search?q=Continuous+Probability+Distribution+ChartCopyright © 2026 Microsoft. All rights reserved. These XML results may not be used, reproduced or transmitted in any manner or for any purpose other than rendering Bing results within an RSS aggregator for your personal, non-commercial use. Any other use of these results requires express written permission from Microsoft Corporation. By accessing this web page or using these results in any manner whatsoever, you agree to be bound by the foregoing restrictions.https://math.stackexchange.com/questions/5114829/continuous-vs-discrete-variablesBoth discrete and continuous variables generally do have changing values—and a discrete variable can vary continuously with time. I am quite aware that discrete variables are those values that you can count while continuous variables are those that you can measure such as weight or height.Sat, 28 Mar 2026 22:48:00 GMThttps://math.stackexchange.com/questions/569928/prove-that-the-function-sqrt-x-is-uniformly-continuous-on-x-in-mathbbr@user1742188 It follows from Heine-Cantor Theorem, that a continuous function over a compact set (In the case of $\mathbb {R}$, compact sets are closed and bounded) is uniformly continuous.Fri, 03 Apr 2026 13:01:00 GMThttps://math.stackexchange.com/questions/477/cardinality-of-set-of-real-continuous-functionsThe cardinality is at most that of the continuum because the set of real continuous functions injects into the sequence space $\mathbb R^N$ by mapping each continuous function to its values on all the rational points. Since the rational points are dense, this determines the function.Thu, 02 Apr 2026 19:14:00 GMThttps://math.stackexchange.com/questions/1182795/what-is-the-intuition-for-semi-continuous-functionsA function is continuous if the preimage of every open set is an open set. (This is the definition in topology and is the "right" definition in some sense.) The definitions you cite of semicontinuities claim that the preimages of certain open sets are open, but does not say so about all open sets. Note that $\ { \ {f \in \mathbb {R} \mid f > \alpha\} \mid \alpha \in \mathbb {R} \} \cup ...Tue, 31 Mar 2026 00:54:00 GMThttps://math.stackexchange.com/questions/75491/how-does-the-existence-of-a-limit-imply-that-a-function-is-uniformly-continuousThen the theorem that says that any continuous function on a compact set is uniformly continuous can be applied. The arguments above are a workaround this.Thu, 02 Apr 2026 21:59:00 GMThttps://math.stackexchange.com/questions/3831023/can-a-function-have-partial-derivatives-be-continuous-but-not-be-differentiableBy differentiability theorem if partial derivatives exist and are continuous in a neighborhood of the point then (i.e. sufficient condition) the function is differentiable at that point.Wed, 01 Apr 2026 17:50:00 GMThttps://math.stackexchange.com/questions/3764351/is-derivative-always-continuousIs the derivative of a differentiable function always continuous? My intuition goes like this: If we imagine derivative as function which describes slopes of (special) tangent lines to points on a ...Tue, 31 Mar 2026 17:22:00 GMThttps://math.stackexchange.com/questions/7923/are-continuous-functions-always-differentiableAn interesting fact is that most (i.e. a co-meager set of) continuous functions are nowhere differentiable. The proof is a consequence of the Baire Category theorem and can be found (as an exercise) in Kechris' Classical Descriptive Set Theory or Royden's Real Analysis.Fri, 03 Apr 2026 12:47:00 GMThttps://math.stackexchange.com/questions/3630336/probability-of-x-y-given-that-x-y-are-i-i-d-continuous-r-v-sThe point is the probability that two continuous random variables assume the same value is $0$ which gives $\alpha = 1/2$. Had they been discrete, then yes one would very much need to account for that probability.Fri, 03 Apr 2026 14:06:00 GMThttps://math.stackexchange.com/questions/2825505/why-not-include-as-a-requirement-that-all-functions-must-be-continuous-to-be-difWe know that differentiable functions must be continuous, so we define the derivative to only be in terms of continuous functions. But then, the fact that differentiable functions are continuous is by definition, while it is being used to justify that very definition.Sat, 28 Mar 2026 18:16:00 GMT