I have a question about one single random variable vs. a bunch of random variables:

If there are n observations from a single RV (call it $X$), and there are n observations in total from n i.i.d RVs (call them $Y_1,Y_2,...,Y_n$), 1 observation from each of the $n$ RVs. The distribution of $Y_n$ is the same as $X$.

Do the two groups of observations have the same distribution?

(If strictly speaking, two groups of observations cannot have distribution because they are not RVs and only RVs can have distribution. So the question is do the two groups of observation have the same mean and variance (or any other statistical parameters) when $n\to+\infty$)

Maybe due to my understanding of RV is not deep enough, I could not find the correct direction to solve the problem. Neither do I know if this question is meaningful or asked correctly.

Any explanation/direction/clarification on definition is very appreciated!

Thanks.

I have a question about one single random variable vs. a bunch of random variables:

If there are n observations from a single RV (call it $X$), and there are n observations in total from n i.i.d RVs (call them $Y_1,Y_2,...,Y_n$), 1 observation from each of the $n$ RVs. The distribution of $Y_n$ is the same as $X$.

Do the two groups of observations have the same distribution?

(If strictly speaking, two groups of observations cannot have distribution because they are not RVs and only RVs can have distribution. So the question is do the two groups of observation have the same mean and variance (or any other statistical parameters) when $n\to+\infty$)

Maybe due to my understanding of RV is not deep enough, I could not find the correct direction to solve the problem. Neither do I know if this question is meaningful or asked correctly.

I have a question about one single random variable vs. a bunch of random variables:

If there are n observations from a single RV (call it $X$), and there are n observations in total from n i.i.d RVs (call them $Y_1,Y_2,...,Y_n$), 1 observation from each of the N RVs. The distribution of $Y_n$ is the same as $X$.

Do the two groups of observations have the same distribution?

(If strictly speaking, two groups of observations cannot have distribution because they are not RVs and only RVs can have distribution. So the question is do the two groups of observation have the same mean and variance when n goes to infinity?)

Maybe due to my understanding of RV is not deep enough, I could not find the correct direction to solve the problem. Neither do I know if this question is meaningful or asked correctly.

Any explanation/direction/clarification on definition is very appreciated!

Thanks.

I have a question about one single random variable vs. a bunch of random variables:

If there are n observations from a single RV (call it $X$), and there are n observations in total from n i.i.d RVs (call them $Y_1,Y_2,...,Y_n$), 1 observation from each of the $n$ RVs. The distribution of $Y_n$ is the same as $X$.

Do the two groups of observations have the same distribution?

(If strictly speaking, two groups of observations cannot have distribution because they are not RVs and only RVs can have distribution. So the question is do the two groups of observation have the same mean and variance (or any other statistical parameters) when $n\to+\infty$)

Maybe due to my understanding of RV is not deep enough, I could not find the correct direction to solve the problem. Neither do I know if this question is meaningful or asked correctly.

Any explanation/direction/clarification on definition is very appreciated!

Thanks.

I have a question about one single random variable vs. a bunch of random variables:

If there are n observations from a single RV (call it X), and there are n observations in total from n i.i.d RVs (call them Y1 to Yn), 1 observation from each of the N RVs. The distribution of Yn is the same as X.

Do the two groups of observations have the same distribution?

(If strictly speaking, two groups of observations cannot have distribution because they are not RVs and only RVs can have distribution.

So the question is do the two groups of observation have the same mean and variance when n goes to infinity?)

Maybe due to my understanding of RV is not deep enough, I could not find the correct direction to solve the problem. Neither do I know if this question is meaningful or asked correctly.

Any explanation/direction/clarification on definition is very appreciated!

Thanks.

I have a question about one single random variable vs. a bunch of random variables:

If there are n observations from a single RV (call it $X$), and there are n observations in total from n i.i.d RVs (call them $Y_1,Y_2,...,Y_n$), 1 observation from each of the N RVs. The distribution of $Y_n$ is the same as $X$.

Do the two groups of observations have the same distribution?

(If strictly speaking, two groups of observations cannot have distribution because they are not RVs and only RVs can have distribution. So the question is do the two groups of observation have the same mean and variance when n goes to infinity?)

Maybe due to my understanding of RV is not deep enough, I could not find the correct direction to solve the problem. Neither do I know if this question is meaningful or asked correctly.

Any explanation/direction/clarification on definition is very appreciated!

Thanks.