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The definition of distribution is(as far as I know) "a function that maps the outcome of an event to it's probability" and all the definitions of random variable I've come across say almost the same. So what is the difference?

MathBun
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  • Citation. Citation. Citation. – User1865345 Jul 24 '23 at 17:15
  • @User1865345-solidarityMods "A random variable is a numerical description of the outcome of a statistical experiment" or "it is a function from possible outcomes in a sample space to a measurable space" – MathBun Jul 24 '23 at 17:32
  • I've never seen a definition of a random variable that says, even approximately, that it's "a function that maps the outcome of an event to it's probability." – jbowman Jul 24 '23 at 17:33
  • "A numerical description" does not equal "it's probability", nor does "a measurable space". – jbowman Jul 24 '23 at 17:33
  • @jbowman, so explain me what is random variable actually is in simple terms – MathBun Jul 24 '23 at 17:34
  • Take a coin flip: heads or tails. The R.V. maps this to 0 or 1, one way or another, but the probabilities aren't 0 or 1. Or "height"; the R.V. maps this to "5'3"", which is not a probability. – jbowman Jul 24 '23 at 17:34
  • @jbowman, so random variable is a function that assigns numbers to the outcomes of an event. Is my definition right? – MathBun Jul 24 '23 at 17:38
  • Not quite, the numbers that can be assigned have to have, collectively, the property of being a measurable space. For most practical purposes, this is ignorable. – jbowman Jul 24 '23 at 17:39
  • This is two questions, because neither definition is correct. For what a random variable is, see https://stats.stackexchange.com/questions/50. For what a distribution is, there are too many posts to mention, but quite a few of the hits on this site search will give you an answer. I suspect your question might originate in multiple senses of "distribution" that include (1) a (discrete) probability distribution and (2) the distribution function of a random variable. – whuber Jul 24 '23 at 19:30

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