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Using the three-bus sample system shown in Figure, assume that the three meters have the following characteristics.

Meter	Full Scale (MW)	Accuracy (MW)	σ(pu)
M₁₂	100	±6	0.02
M₁₃	100	±3	0.01
M₃₂	100	±0.6	0.002

a. Calculate the best estimate for the phase angles θ1 and θ2 given the following measurements.

Meter	Measured Value (MW)
M12	60.0
M13	4.0
M32	40.5

b. Calculate the residual J(x). For a significance level, a, of 0.01, does J(x) indicate the presence of bad data? Explain.

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