# Thread: independent identically distributed R. V's

1. ## independent identically distributed R. V's

If ${X_i}$ for $i=1,...n$ are $i.i.d$, then can we show that ${X_i ^2}$ for $i=1,..n$ are also $i.i.d$?

2. yup

Whatever you had for the distribution of X, your new random variables $Y_i=X^2_i$

will all have that new distribution.

And also if $X_i$ is independent of $X_j$ for $i\ne j$

then $X_i^2$ is independent of $X_j^2$ for $i\ne j$

3. ## iid

is there a way to show that $X_i^2$ are independent?

4. do you want a measure theoretical proof or for just continuous or discrete rvs?

5. ## iid

any one of those is fine. thank you very much

6. Think about the independence of the sigma-algebras generated by each of the random variable