Timeline for Show that the two random variables with F-distribution are independent
Current License: CC BY-SA 4.0
4 events
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| Feb 25, 2023 at 6:00 | comment | added | TryingHardToBecomeAGoodPrSlvr | With regards to the addition (proof of part (a)), it's a cool thing to express it in terms of spherical co-ordinates. Most of mathematics/problem solving is about seeing "how things move" or "recognizing certain structure" in a given mathematical setup and in this instance, these RVs looked at as co-ordinates helps a lot. Thanks for sharing it with us! | |
| Feb 24, 2023 at 17:13 | history | edited | Zhanxiong | CC BY-SA 4.0 |
added 1360 characters in body
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| Feb 24, 2023 at 14:48 | comment | added | TryingHardToBecomeAGoodPrSlvr | Thank you. Also, the thing is that if we know $Z_1=X_1/X_2$, $Z_2=X_1+X_2$, and $X_3$ are mutually independent, then $Z_1$ and $f(Z_2,X_3)$ are independent for any measurable function $f$. I was looking at an inconvenient triplet but as it turns out, the right triplet to consider was $Y_1$, $Y_2$ and $X_3$. That's where I went wrong. :( | |
| Feb 24, 2023 at 13:32 | history | answered | Zhanxiong | CC BY-SA 4.0 |