New answers tagged

0 votes

Statistical test for small non-parametric dataset with more than 2 dependent groups

With censored response, survival analysis is useful and probably the more appropriate one. See https://stackoverflow.com/questions/41968606/left-censoring-for-survival-data-in-r for both left and ...
DrJerryTAO's user avatar
  • 1,325
2 votes

A and B are independent. Does P(A ∩ B|C) = P(A|C) · P(B|C) hold?

A related question is If $X, Y$ are independent of $Z$, is $P(X|Y, Z) = P(X|Y)$? The example there, $C = XOR(A,B)$, is a simple counter example to this question as well ...
Sextus Empiricus's user avatar
22 votes

A and B are independent. Does P(A ∩ B|C) = P(A|C) · P(B|C) hold?

No this is not in general true, as you can see from a simple counter example: Toss two independent coins. Event $A$ is coin 1 head. $P(A)=0.5$ Event $B$ is coin 2 head. $P(B)=0.5$ Event $C$ is either ...
George Savva's user avatar
  • 2,034
2 votes

Can we conclude from $\DeclareMathOperator{\E}{\mathbb{E}}\E g(X)h(Y)=\E g(X) \E h(Y)$ that $X,Y$ are independent?

This is almost Proposition 7.1.3(i) from Athreya & Lahiri 2006 sans some minor differences in formatting: Let $(\Omega, \mathcal{F}, P)$ be a probability space and let $\{X_1, \ldots, X_k \}$, $2 ...
Galen's user avatar
  • 8,095
0 votes

Joint probability of a minimum and maximum score after $n$ dice rolls

Please find the answer attached in the image below.
viddie's user avatar
  • 1

Top 50 recent answers are included