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Is the exponential distribution (i.e. as in https://en.wikipedia.org/wiki/Exponential_distribution ) a "continuous probability distribution"?

If answer "no", can someone explain why not and yet why, say, a continuous uniform distribution is a "continuous probability distribution"?

Reason for my question:

Up until recently, I had always thought the word "continuous" in the term "continuous probability distribution" was indicating that the "probability distribution" is FOR a "continuous random variable". But then someone in a science forum made me doubt that and insists that it isn't but its there to indicate that the "function is continuous", but I didn't get his meaning. And, contrary to what I always thought, he insists that the exponential distribution is NOT a "continuous probability distribution" because it is "not continuous". But, again, don't get what he means. Is he right? If so, explain.

First: It says right in the introduction to the Wikipedia article that this is a continuous distribution. So your answer is right there. You are correct. Further, you are correct entirely. Your definition is entirely correct:

That is a true, correct, and essentially complete characterization of what it means to be a continuous probability distribution.

Now, to elaborate.

A continuous probability distribution is one in which the associated random variable is continuous (i.e. not discrete).

See:

All of the above definitions are satisfied by the exponential distribution except the one from "Probability for Dummies" (second to last). I have underline the incorrect part of their definition. Perhaps your friend is a dummy? Perhaps "Probability for Dummies" was written by dummies? It is possible they meant to state what the last definition (from Wikipedia) says, which is that the

The function that describes the probability distribution function of the exponential distribution is not a continuous function. It is zero for values x<0 and λe^(-λx) for x≥0, causing a jump discontinuity in the function.

However,

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Comment | Thanks for that. I am pretty relieved as he seriously made me doubt myself! I will now go back to him on that science forum and present him with this info and see what he says. |

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