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max of Z1, Z2, Z3, Z4

where

Z1 = |X1+X2+X3|^2 + |Y1+Y2+Y3|^2

Z2 = |X1-X2+X3|^2 + |Y1-Y2+Y3|^2

Z3 = |X1+X2-X3|^2 + |Y1+Y2-Y3|^2

Z4 = |X1-X2-X3|^2 + |Y1-Y2-Y3|^2

Xi, Yi are independent zero mean normal with variance 1/2.

So, Z1,Z2,Z3,Z4 are indentically distributed exponential random variables,

But they are correlated.

Can anybody help me?