Question

At a high school cross country race, runners are randomly issued 3-digit numbers to wear as they run the race. All runners will start the race at the same time. As runners finish the race, their finishing order will be recorded by recording their numbers as they cross the finish line. What correlation should exist between the runners' numbers and the order in which they finish the race?

Answer 1

There is not enough information to determine what type of correlation will exist between the runners' numbers and the order in which they finish the race.

Answer 2

\[
\rho_{X,Y}=\frac{\text {Cov}(X,Y)}{\sigma_X\sigma_Y}
\]We'd expect that \(\text {Cov}(X,Y)=0\) among independent events, so we should then expect \(\rho_{X,Y}= 0\)

Answer 3

\(\rho\) stands for correlation, while \(\text{Cov}\) stands for covariance.

Answer 4

There isn't much info given

Answer 5

thanks ! !!!! :)

Answer 6

@UditKulka It says \(should\). Like "what should happen if you flip a coin twice"

Answer 7

You should get 50% heads but that might not necessarily be the case.

Answer 8

Theoritcally Much info isn't given

U need some values to plot a graph

Answer 9

Here is a potential graph:

Answer 10

You don't need any points theoretically.

Answer 11

Independent events have no correlation.

Answer 12

So u say there is no correlation

Answer 13

But that might not be a neccesity @wio

Answer 14

But it's a theoretical question.

What would you say then?

Answer 15

If it is a theorotical question How do we plot a graph theorotically u can't assume

Answer 16

You don't need to plot a graph.

You can run a simulation. It will tend towards 0.

Answer 17

i didn't get u