2
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Given any events $A$,$B$ and $C$ where $A$ and $B$ are independent, is it true that $P(A|B\cap C) = P(A|C)$?
This conjecture is not true. One easy way to see this is that while $P(A|C)$ is well defined as long as $P(C) > 0$, $P(A|B\cap C)$ could well be undefined because $P(B \cap C)$ may vanish (e.g., ...
- 16.5k
2
votes
Accepted
Source for Bernstein's example for pairwise independence
Requested from comments:
https://maa.org/sites/default/files/Stepniak-1-0734037.pdf gives the reference as p.47 of "S. N. Bernstein, Theory of Probability, 4th ed. (in Russian), Gostechizdat, ...
- 37.2k
1
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Two events, both of probability zero, have caused an outcome of probability zero. Which of them did happen?
Let me answer your "broader question" first because it is less technical. There are many ways to show $XY$ and $YZ$ are not independent given $X, Y, Z \text{ i.i.d. } \sim N(0, 1)$. For ...
- 16.5k
1
vote
Accepted
How to consider independent samples in a mixed-design experiment?
In this type of design, involving repeated measures, because of the interplay between between-subjects factors (the two populations) and within-subjects factors (the differing conditions for each ...
- 56.6k
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