Thread: Confused with basic terms:iid, rv

are iid rvs with and

I need to make sure my understanding of this statement is correct.
If X is a rv, then it is a function defined over a sample space.
i = 1,2,3,....n constitute the number of trials of this rv.
are not random variables, but values which the random variable (a function) assumes.

So here's my confusion.

If is only a value, analogous to the range of a function, say, , what is the actual meaning of
and ? Is it just trying to imply that these values are all drawn from a RV whose parameters are and ?

Are they liberal with the semantics or is my understanding wrong?

Thanks for your time!

Originally Posted by chopet

are iid rvs with and

I need to make sure my understanding of this statement is correct.

Usually, random variables are written in block capitals, that's why this definition is a bit confusing. In fact, are independent copies of a random variable , i.e. they are independent identically distributed random variables (and their common distribution is that of ). This is the way to model " values drawn from a random variable ", as you wrote. For a given sample , a random variable assumes only one value . When modeling several independent repetitions an experiment (like throwing a coin), the sample space has to be widened so that it contains the values of every sequence that can appear. Numerical observations would be for some in the sample space.

I hope this makes things clearer...
Laurent.

yes, they do. Thanks.