# What is an example of a chi-squared distribution?

I'm trying to figure out the usage of the $\chi^2$ distribution. In other words, in what kind of situations it occurs and how is it useful in that situations.
I read the wikipedia definition of $\chi^2$. Can someone give an example of a $\chi^2$ distribution so that I can better understand it?

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@Can't Tell: I think there is no rationale behind the chi-square distribution. You can see it as a sum of N(0,1)^2. You can also characterise it via its pdf. The reason why it is introduced is that important test statistics follow that distribution, at least approximately. For instance, the likelihood ratio. –  ocram Mar 13 '11 at 13:21
@Marco: Thanks for your comment. But I'm not very good with statistics and I don't understand what you mean by sum of N(0,1)^2 or "likelihood ratio". What I was looking for was something like "if you take the case X, the variables Y and Z are independent standard normal random variables and if you plot the values A and B, then that would be a Chi Square distribution." Is such an example possible(with X,Y,Z,A and B)? –  Can't Tell Mar 13 '11 at 13:27
@Can't Tell. I am not sure to get what you exactly want. But take two independent standard normal random variables. Square them and add them. This results in a chi-square random variable whose parameter is 2. If you had had 3 normal variables, the parameter would have been 3, etc. –  ocram Mar 13 '11 at 13:34
@Can't What does it mean to "understand" a distribution? As it stands, this question seems rather personal and idiosyncratic in that regard. Could you rephrase it so that it might be meaningful to other people? –  whuber Mar 14 '11 at 4:50
@whuber: I edited the question. Do you think it is okay now? –  Can't Tell Mar 14 '11 at 6:55
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