# "A discrete random variable must have a finite range." Is this true? Provide examples where possible [duplicate]

new to the community here and this topic on random variables. This was a discussion question posed to my group, and I have difficulties answering the question. I know that discrete means that its countable, but thats about it.

I saw the question posed called "Properties of a discrete random variable" but it didn't do much help for me.

Many thanks for reading this question.

• No. Consider the Poisson distribution. Aug 5 '19 at 2:32
• Wikiepedia's list of some Discrete distributions with infinite support. Possible duplicate of 1. stats.stackexchange.com/questions/60666/… and 2. stats.stackexchange.com/questions/368885/… Aug 5 '19 at 3:21
• Also see answers to this question on reddit only about a day ago: Must a discrete random variable have a finite range?. If that's your question (and it looks almost identical), then you already got good answers there (with examples). If you still have remaining questions after reading the linked posts and Wikipedia's list, please post a new question. Aug 5 '19 at 3:33
• You mention in your question you read the answers here: Properties of a discrete random variable but that it wasn't much help. The top answer - i.e. most upvoted (& also accepted) answer - there includes the following as its 2nd and 3rd paragraphs: "While discrete distributions can have a finite number of possible outcomes, they are not required to; you can have a discrete distribution that has an infinite number of possible outcomes - the number of elements should be no more than countable." ... ctd Aug 5 '19 at 3:43
• ctd... "A common example would be a geometric distribution; consider the number of tosses of a fair coin until you get a head. There's no finite upper bound on the number of tosses that may be needed. It may take 1 toss, or 2, or 3, or 100, or any other number." ... how are those two paragraphs not a complete answer to this question? What confusion does that explicit answer and example leave you with? Aug 5 '19 at 3:43