Two ideal dice are thrown . Let X1 be the score on the first die and X2 be the score on the second die. Let Y = max(X1, X2) then
(i) Evaluate Corr(Y, X1).
(ii) Evaluate Corr(Y, X2).
In throwing two dice,
"S=\\{(1,1),(1,2)...(1,6)\n\\\\(2,1),...,(2,6)\n\\\\.\n\\\\.\n\\\\ (6,1),...(6,6)\n\n\\}"
X1=score on 1st die.
X2=score on 2nd die.
Y=max(X1,X2)
Thus, we have:
X1={1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,6,6,6,6}
X2={1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6}
Y={1,2,3,4,5,6,2,2,3,4,5,6,3,3,3,4,5,6,4,4,4,4,5,6,5,5,5,5,5,6,6,6,6,6,6,6}
(i):
Corr(Y, X1)
X1 Values
∑ = 126
Mean = 3.5
∑(X1 - Mx)2 = SSx = 105
Y Values
∑ = 161
Mean = 4.472
∑(Y - My)2 = SSy = 70.972
X and Y Combined
N = 36
∑(X1 - Mx)(Y - My) = 52.5
R Calculation
"r = \u2211((X1 - My)(Y - Mx)) \/ \\sqrt{(SSx)(SSy)}\n\n\\\\\nr = 52.5 \/ \\sqrt{(105)(70.972)} = 0.6082"
(ii):
Corr(Y, X2) = 0.6082
It is same as Corr(Y, X1) because X1 and X2 contains same and equal number of observations.
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