Timeline for does convolution of a probability distribution with itself converge to its mean
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Feb 11, 2022 at 16:48 | comment | added | dodo | @Emma The probability at the mean (0.5) is also approaching zero percent. Can you fig it out? | |
| Feb 11, 2022 at 7:24 | comment | added | Emma | @dodo I don't see it from this example. To simplify the notation I write Y1 as (1,25%; 0.5,50%;0,25%). I get Y2= (1,6.25%; 0.75,25%; 0.5,37.5%;0.25,25%,0,6.25%). Indeed 0.5 has a lower probability than 50%. But the weighted sum of other values(e.g, 0.75) would converge to 0.5. Or if they do not (e.g, as 1 or 0 in this example), they corresponding probabilities would approach to 0. | |
| Feb 10, 2022 at 17:52 | comment | added | whuber♦ | This does not demonstrate lack of convergence, however! It is quite possible for every random variable in a sequence to have zero chance to equal their common mean, yet for that sequence to converge to a constant. The standard example is a sequence of averages of iid standard Normal variables. | |
| S Feb 10, 2022 at 17:33 | review | First answers | |||
| Feb 10, 2022 at 23:47 | |||||
| S Feb 10, 2022 at 17:33 | history | answered | dodo | CC BY-SA 4.0 |