Timeline for Minimizing the expected time to get a string of heads with biased coins
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 24, 2023 at 15:55 | comment | added | Lorenzo Pompili | I agree with $E$ being the fraction you wrote. The rest looks right as well | |
| Jan 24, 2023 at 3:41 | comment | added | S. Green | This makes me think the full optimization problem is too hard, as it requires considering the constraint $p_i \in [0, 1]$ too carefully. It may be easier to consider the problem where $\alpha = \frac{n}{2}$, in which case it seems unlikely that any $p_i > 1$ using the optimization procedure. I am able to obtain numerical results using a standard optimizer, and I imagine the answers are the roots of some polynomial (as in the $n=2$ case), but I don't see what polynomial. | |
| Jan 24, 2023 at 3:05 | history | answered | Henry | CC BY-SA 4.0 |