Timeline for Proof that the probability of one RV being larger than $n-1$ others is $\frac{1}{n}$
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 16, 2015 at 3:54 | comment | added | Dilip Sarwate | Starting from $\sum_i\Pr(M_i)=1$, we have that the average value of these $n$ probabilities is $\frac 1n$. Now, without loss of generality, suppose that there exists a proof that $\Pr(M_1)>\frac 1n$. Then, by interchanging subscripts $1$ and $i$ in the proof, we can show that $\Pr(M_i)>\frac 1n$ and similarly $\Pr(M_j)>\frac 1n$ and $\ldots$, leading to the conclusion that we are either in Lake Wobegon where all the $\Pr(M_j)$ are above average in value, or that the proof that $\Pr(M_1)>\frac 1n$ is faulty, and that all the $\Pr(M_i)$ must necessarily have the same value $\frac 1n$. | |
| Jan 15, 2015 at 22:58 | comment | added | whuber♦ | +1 This is definitely the easy and insightful way to see why the result is true, and your rigor is helpful. | |
| Jan 15, 2015 at 22:43 | history | edited | Danica | CC BY-SA 3.0 |
typo
|
| Jan 15, 2015 at 22:31 | history | answered | Danica | CC BY-SA 3.0 |