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I have a little problem with understanding of the concept of independent identically distributed random variables. Random variable is a function that assigns some values to the all events from sample space. If I roll the dice then I have one random variable available, because there are numbers on the sides of if, so there is an assignment. No I understand that if i want to have another random variable then I should create another assignment ... so for example I can assign +2 to every wall. So I have two independent identically distributed random variables ... one which assigns values from 1 to 6 and second which assigns values between 3 and 8 ... right?

Then if I roll the dice five times in two series, and I use the same wall-value assignment can I treat every series as different random variable, so data from first series are independent identically distributed random variables from data from second series or should I treat it as one random variable? Can random variable be treated as series of data ?

I ask because central limit theorem says that distribution of the average of $n$ iid is close to normal distribution, so if I want to achieve this distribution I should always use different random variables, or simple different series of data with the same event-value assignment function ?

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Your two random variables are not identical distributed. For example $P(X_1=1)=\tfrac{1}{6}$ but $P(X_2=1)=0$, where $X_1$ is the random variable assigning values 1 to 6 and $X_2$ is the one assigning values 3 to 8. –  Stefan Hansen Mar 30 '12 at 17:02
Ok, and what about series of data, can I treat data from two series as data from two iid random variables ? –  Darqer Mar 30 '12 at 17:21
It depends on the sources of the data. If there is no conceivable source of dependence, they can be treated as independent. –  Robert Israel Mar 30 '12 at 18:10

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