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Describe the distribution of e hence or otherwise find the

You take measurements for a location in 3D space. Your measurement errors in each dimension, e_X, e_Y and e_Zare all Gaussian with zero mean and variance ?². The total squared error is E = e_X² + e_Y² + e_Z²_. Describe the distribution of E. Hence, or otherwise, find the mean and variance of E? What is a 90% confidence interval for E as a factor of ?^2.

HINT: which distribution is constructed by summing Z scores?

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