independent identically distributed R. V's

**Kat-M** · September 27th 2009, 06:58 PM

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 $i.i.d$ ?

**matheagle** · September 27th 2009, 07:15 PM

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 $i\ne j$

**Kat-M** · September 27th 2009, 10:10 PM

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

**matheagle** · September 27th 2009, 10:13 PM

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

**Kat-M** · September 27th 2009, 10:28 PM

any one of those is fine. thank you very much

**Moo** · September 28th 2009, 10:02 AM

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

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