Answer:
The proof is in the explanation below.
Step-by-step explanation:
Data:
Let N cards have different numbers: x₁, x₂,x₃.....xn
To calculate the correlation coefficient p, let the two random variable be defined as C₁ and C₂.
These variables represent the different number x₁ on the card 1 and card 2 respectively.
Let also the indicative factors be [tex]I_{C1=X1}[/tex] and [tex]I_{C2 = x1}[/tex]
Therefore:
E[1C1=xi]=Pr[C1=xi]=1N
E[1C2=xi]=Pr[C2=xi]=Pr[C2=xi∣C1≠xi]Pr[C1≠xi]=1NandE[1C1=xi1C2=xj]=Pr[C1=xi∩C2=xj]= -1(N−1)
