# Thread:

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
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 14, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9287089705467224, "perplexity_flag": "middle"}