# Compute $\text{Corr}(X_{11},X_{12})$ where $X_n$ is the number of the $n$th ball drawn from a basket of $100$ balls

There are 100 balls in a basket numbered 1,2...,100. 12 balls are being pulled out one after another without return. Let $X_i$ be the value on the i'th ball. Calculate $\text{Corr}(X_{11},X_{12})$

Obviously the numbers on the balls are very dependent on each other, so i don't know how to begin to calculate their expected values. Actually i don't know how to represent these variables, no known distribution comes to mind. Can anyone help?

• Say you want to find E($X_4$). Observe $X_4$ is uniformly picked up from {1,2,...100}\{$X_1 , X_2 ,X_3$}. Given X1,X2 and X3 you can find the expectation...so try to use E(X) = E(E(X| Y))..it may be helpful.. – Horan May 27 '17 at 7:35
• The ranks $11$ and $12$ are a decoy. Note simply that $(X_{11},X_{12})$ is uniform on $\{1,2,\ldots,100\}^2$ minus the diagonal, and proceed. – Did May 27 '17 at 9:01
• @Horan To compute $E(X_4)$, I would certainly not follow your hint, sorry. – Did May 27 '17 at 9:01
• @Did I see what you're saying but we haven't learned these methods – CodeHoarder May 27 '17 at 9:16
• Since the word "symmetry" does not suffice (but perhaps did you miss it?), my suggestion at this point would be that you carefully compute, say, $$P(X_3=42)$$ What do you find? – Did May 28 '17 at 6:26