Talk:Random variable

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Contents 1 Delete example? 2 Definition 3 Examples 4 Minimal meanderings on meta-definintions 5 Definition of cumulative distribution function 6 Reverted change to definition 7 A question about Equality in mean 8 A 'first iteration' simple explanation possible? 9 Other definition

[edit] Delete example?

Would it be appropriate to delete the "example" section at the bottom? 203.173.32.84 06:52, 22 Mar 2005 (UTC)

I think so, don't see what it adds. Frencheigh 08:20, 22 Mar 2005 (UTC)

Yes. Moreover, it is not an example of random variable. Its just a realization of random variable. Hardly misleading. --140.78.94.103 17:59, 24 Mar 2005 (UTC)

[edit] Definition

I dont like the definition here, not that I'm letting my ignorance of stats stop me from commenting, but could this be considered a clearer definition?:

"Random Variable

The outcome of an experiment need not be a number, for example, the outcome when a coin is tossed can be 'heads' or 'tails'. However, we often want to represent outcomes as numbers. A random variable is a function that associates a unique numerical value with every outcome of an experiment. The value of the random variable will vary from trial to trial as the experiment is repeated.

There are two types of random variable - discrete and continuous.

A random variable has either an associated probability distribution (discrete random variable) or probability density function (continuous random variable).

I think this is definitely an improvement but it should be pointed out that there exists r.v.'s which are neither discrete nor continuous (for example take the sum of one r.v. of each type) Brian Tvedt

[edit] Examples

1. A coin is tossed ten times. The random variable X is the number of tails that are noted. X can only take the values 0, 1, ..., 10, so X is a discrete random variable.
2. A light bulb is burned until it burns out. The random variable Y is its lifetime in hours. Y can take any positive real value, so Y is a continuous random variable.

"

I think the above definition (for the original reference, pls search via google) explains to me that it is a mapping between a value and the sequence number of that value, rather like a numeric index to a database record. This would appear to allow greater generalization in statistical definitions and algorithms. The earler Wikiedia definition led me to comment on another Wikipedia definition incorrectly because I think I may have misunderstood the concept after looking at this Wikipedia definition.

[edit] Minimal meanderings on meta-definintions

In relation to the above, comparing the two definitions, one seems more mathematically formal than the other. We should probably bear in mind when posting (not that I've done much), that one's definition should stand on it's own as far as possible. That is, it should be very comprehensible to an everage target reader in a minimum time. This means we may need to take great care when using references to other definitions and also avoid overly specialised terms. This is not to suggest that relevant specialised references should be avoided. Often experts in a field may use highly specialised terms in a definition as they are most familiar with that definition, although it may not be the most suitable for the general reader. This probably means, amongst other things, that we should try to use plain language to describe the concept as far as possible, together-with/based-on a minimum number of external definitions/explanatory references, especially those external to Wikipedia. Perhaps this comment could be added to the general rules for posting as a form of guidance.

[edit] Definition of cumulative distribution function

I have edited the page to consistently use the right-continuous variant (using less-than-or-equals as opposed to less-than) for the cumulative distribution function. This is the convention used in the c.d.f. article itself.

Also, I fixed was a minor error in the example, in that it implictly assumed the given r.v. was continuous. For what it's worth, I agree that the example adds little to the article and should be deleted. Brian Tvedt 03:05, 14 August 2005 (UTC)

[edit] Reverted change to definition

The change I reverted was:

The expression "random variable" is an embarrassingly dogmatic misnomer: a random variable is simply a function mapping from events to numbers.

It's not so simple. A random variable has to be measurable. Also, the opinionated tone is not appropriate.Brian Tvedt 01:06, 21 August 2005 (UTC)

[edit] A question about Equality in mean

Why is "Equality in mean" as defined in 4.2 different from "Almost sure equality" ? A nonnegative random variable has vanishing expectation if and only if the random variable itself is almost surely 0, no ? Apologies if I missed a trivial point. MBauer 15:48, 28 September 2005 (UTC)

Yes, that seems the same.--Patrick 20:20, 28 September 2005 (UTC)

[edit] A 'first iteration' simple explanation possible?

In the first paragraph I find: " For example, a random variable can be used to describe the process of rolling a fair die and the possible outcomes { 1, 2, 3, 4, 5, 6 }. Another and the possible outcomes { 1, 2, 3, 4, 5, 6 }. Another random variable might describe the possible outcomes of picking a random person and measuring his or her height." I am not at all sure what the random variable *is* in these two cases from the description. How does a rnd.var. describe a process? Isn't it the result of a process that it pertains to? How does a rnd.var. *describe* the possible outcomes? My understanding is that it could be e.g. the number of dots facing upwards in an experiment being one throw of a die (but what about a coin? head/tail is not a number, or for a die with different color faces?), or e.g. the number of occurances of the die showing a '1' in a given number of throws. In the second example, I guess it is the height of a person that is the rnd.var. Again I'm not sure how this *describe* the possible outcomes, I thought the 'range' of possible outcomes would be the interval from the height of the lowest person in a population to the highest, and I don't see how a rnd.var. *describe* this. What I often miss in definitions are some simple, yet precise descriptions and examples, before the more elaborate definitions, which are often too technical to be helpful at first (but good to visit later when my understanding of the subject has grown). Could anybody with a better knowledge of the subject please change/amend the introduction? Thank you. M.Andersen

80.202.85.143 11:07, 9 August 2006 (UTC)

I think it will be convenient to have sections in discussion pages in order to manage different questions around the same subject. Appart from this suggestion, I sincerely think that the text at the begining of the article is circular. Indeed, saying that "a random variable is a function that maps results of a random experiment..." is saying nothing. I agree with the ponit that "we should try to use plain language to describe the concept as far as possible...". But I think it must be clear when we are describing (informally) a subject and when we are defining (formally) the same thing. The correct definition is allredy on the text but it begans with an horrible "Mathematically, a random variable is..." If we introduce, in mathematical subjects, a section of informal description and a section of formal definition, I think we will gain in clarity. I will not change the subject attending comments on my suggestion. --Crodrigue1 15:54, 19 November 2006 (UTC)

[edit] Other definition

==Incorrect sentence - "random variable"==

I don't think this sentence is correct:

Some consider the expression random variable a misnomer, as a random variable is not a variable but rather a function that maps outcomes (of an experiment) to numbers

.. A random variable is a variable... a value that can take on multiple different values at different times. It is NOT a function. A function could describe the rate at which that random variable takes on different values. They aren't the same thing. Just like an object in space or a thrown ball aren't the same things as the functions that describe their trajectories. Fresheneesz 07:05, 29 January 2007 (UTC)

Looking into it further, I think that there are two different definitions of a "random variable". In statistical experiments, you hold as many variables constant so that you can study a very few (preferably just one) variable. This variable *will* be random with some probability distribution. This is not the random variable that this article is talking about.

My question is: whats the difference between this and a probability distribution? We should add a second page covering the other definition or at least put a note on this article. Fresheneesz 07:11, 29 January 2007 (UTC)

Well, when you formalize things, a random variable becomes nothing than a measurable function. In the same way as a probability becomes nothing than a kind of measure. Oleg Alexandrov (talk) 16:07, 29 January 2007 (UTC)

I suppose. Well, I think some effor needs to go into reconciling these two mergable ideas of a "random variable" and a "random function" so that either definition will be consistant with the one in the aritcle. Fresheneesz 21:08, 5 February 2007 (UTC)