Timeline for Draw two numbers, A and B, from a set {1, 2, 3, 4, 5, 6}. A and B are drawn sequentially without replacement. Find the variance Var(3A+B).
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Oct 6, 2022 at 1:02 | comment | added | Advay Mansingka | @GrahamKemp Thank you for the comment, this is very helpful! I think (hopefully?) I have a better understanding of the distinction between identical and independent now | |
| Oct 5, 2022 at 0:18 | comment | added | Graham Kemp | @AdvayMansingka They are not independently distributed as you noticed. However they are identically distributed due to symmetry. You are drawing two elements from the set and calling one $A$ and the other $B$. The order in which $A,B$ are labelled is not important. Identical distribution just means for all $k$ in $\{1,2,3,4,5,6\}$ that $\mathsf P(A=k)=\mathsf P(B=k)$ | |
| Oct 4, 2022 at 19:21 | comment | added | Advay Mansingka | Thanks for the answer! Could you help me better understand why A and B are identically distributed in this case? The way I have been approaching it is that B is dependent on A because B can only be drawn from the numbers left in the set after A is drawn. For example, if A=1, it is not possible for B=1 however if A, B are iid then P(A=1, B=1) > 0. Am I incorrect in how I am understanding the concept of iid? Thanks again! | |
| Oct 4, 2022 at 19:17 | vote | accept | Advay Mansingka | ||
| Oct 4, 2022 at 6:28 | history | answered | Parcly Taxel | CC BY-SA 4.0 |