Question

From a box of fruit containing 62 oranges and 1 apple a random sample of 2 pieces of fruit has been selected without replacement. Let X be the number of oranges and Y be the number of apples in the sample. What will the correlation of X and Y be?  

(Hint the variance of X and Y same.

Covariance is just negative of these variances. )

Answer 1

from above:

x	y	f(x,y)	x*f(x,y)	y*f(x,y)	x^2f(x,y)	y^2f(x,y)	xy*f(x,y)
1	1	2/63	0.0317	0.0317	0.0317	0.0317	0.0317
2	0	61/63	1.9365	0.0000	3.8730	0.0000	0.0000
	Total	1	1.9683	0.0317	3.9048	0.0317	0.0317
	E(X)=ΣxP(x,y)=					1.9683
	E(X2)=Σx2P(x,y)=					3.9048
	E(Y)=ΣyP(x,y)=					0.0317
	E(Y2)=Σy2P(x,y)=					0.0317
	Var(X)=E(X2)-(E(X))2=					0.0307
	Var(Y)=E(Y2)-(E(Y))2=					0.0307
	E(XY)=ΣxyP(x,y)=					0.0317
	Cov(X,Y)=E(XY)-E(X)*E(Y)=					-0.0307
	Correlation ρxy=Cov(X,Y)/sqrt(Var(X)*Var(Y))=					-1.0000