Timeline for Expected Value of Maximum of Uniform Random Variables
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 14, 2022 at 6:10 | answer | added | Hassan Nazari | timeline score: 0 | |
| Jan 13, 2022 at 19:37 | comment | added | whuber♦ | I find it helpful to work with a simpler way of expressing the numbers: adopt a system of measurement in which the origin is at $200$ and $400$ is one unit. Your variables are uniform on $[0,1]$ in this system, whose CDF is $x$ (for $0\le x\le 1$), whence the CDF of their maximum is $x^3$ (for $0\le x\le1$) and therefore the expectation is $\int_0^1(1-x^3)\mathrm{d}x=3/4.$ This is the formula you tried to use. In these new units it's harder to make a mistake in the computations. In the original units, $3/4$ is equivalent to $200 + 3/4\times 400=500:$ it's now obvious what was missing. | |
| May 13, 2020 at 2:01 | vote | accept | Kitsune Cavalry | ||
| May 13, 2020 at 1:56 | answer | added | Lucas Roberts | timeline score: 5 | |
| May 13, 2020 at 1:34 | history | asked | Kitsune Cavalry | CC BY-SA 4.0 |