Timeline for Understand the linearity of the expected value operator
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Jul 28, 2023 at 16:48 | history | edited | Dave Ray | CC BY-SA 4.0 |
Fixing some typos
|
| S Jul 28, 2023 at 16:48 | history | suggested | alexis_thual | CC BY-SA 4.0 |
Fixing some typos
|
| Jul 28, 2023 at 13:53 | review | Suggested edits | |||
| S Jul 28, 2023 at 16:48 | |||||
| Jul 28, 2023 at 13:28 | comment | added | Zhanxiong | Writing something like "$d(x + y) = dx + dy$" in the integral is a common misunderstanding to the expectation formula. See this long related discussion/clarification for a similar and slightly more general problem. | |
| Jul 28, 2023 at 10:45 | answer | added | alexis_thual | timeline score: 2 | |
| Jul 28, 2023 at 5:54 | history | edited | Dave Ray | CC BY-SA 4.0 |
added 1067 characters in body
|
| Jul 27, 2023 at 17:20 | comment | added | whuber♦ | The expectation is the probability-weighted average value (mean). The Distributive Law of Arithmetic implies the mean of a sum is the sum of the means. That's all there is to it. The answer at math.stackexchange.com/questions/1810365 is complete and rigorous but when you inspect it closely you realize it comes down to the assertion that the (Lebesgue) integral is linear -- and that ultimately is proven by analyzing step functions, which reduce the problem to what I just stated. | |
| Jul 27, 2023 at 16:52 | history | edited | User1865345 |
edited tags
|
|
| Jul 27, 2023 at 16:34 | answer | added | Xi'an | timeline score: 3 | |
| Jul 27, 2023 at 16:34 | comment | converted from answer | alexis_thual | I think the left side of your equation is ill-formutated. You might be interested in this discussion about the linearity of the expectation operator: https://math.stackexchange.com/questions/1810365/proof-of-linearity-for-expectation-given-random-variables-are-dependent | |
| Jul 27, 2023 at 16:20 | comment | added | Peter Flom | Welcome to the site. I added codes to format the formulas. Please check that this is how you want it. | |
| Jul 27, 2023 at 16:19 | history | edited | Peter Flom | CC BY-SA 4.0 |
Added codes to make it LaTeX
|
| S Jul 27, 2023 at 16:16 | review | First questions | |||
| Jul 27, 2023 at 16:35 | |||||
| S Jul 27, 2023 at 16:16 | history | asked | Dave Ray | CC BY-SA 4.0 |