Consider X,..., X, id N(, o Id), where Id is the d x d identity matrix....

 

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Consider X₁,..., X, id N(μ, o² Id), where Id is the d x d identity matrix. Let Xn be the sample average. Using the sub-exponential tail bound, show that with probabiltiy at least 1-8, o²d| |X - H²2² = 0 (² log(2/6) + μ|| - n n n √dlog (2/8) [Hint: First show that n||Xn − µ||²/0² is a chi-square random variable.] - Consider X₁,..., X, id N(μ, o² Id), where Id is the d x d identity matrix. Let Xn be the sample average. Using the sub-exponential tail bound, show that with probabiltiy at least 1-8, o²d| |X - H²2² = 0 (² log(2/6) + μ|| - n n n √dlog (2/8) [Hint: First show that n||Xn − µ||²/0² is a chi-square random variable.] -

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Solution First we note that Xn u 2nX where X is iid standard normal Therefore nX... View the full answer