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Q10Section A (Section A)10 of 15

Correlation between a sum of two normals and the total of eight

Let X1,…,X8X_1,…,X_8 be i.i.d. N(0,σ2)N(0,\sigma^2) random variables. Further, let U=X1+X2U=X_1+X_2 and V=∑i=18XiV=\sum_{i=1}^8X_i. The correlation coefficient between UU and VV is

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