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Consider a D-dimensional Gaussian random variable x with distribution N(x|,) in which the covariance matrix is known and for which we wish to infer the mean from a set of observations X = {x1, . . . , xN}. Find the ML estimate of . Given a prior distribution p() = N(|0,0), find the corresponding posterior distribution p(|X), and the MAP estimate of ..

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Consider a D-dimensional Gaussian random variable x with distribution N(x|,) in which the covariance matrix is known and for which we wish to infer the mean from a set of observations X = {x1, . . . , xN}. Find the ML estimate of . Given a prior distribution p() = N(|0,0), find the corresponding posterior distribution p(|X), and the MAP estimate of .

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Consider a D-dimensional Gaussian random variable x with distributio.pdf

  • 1. Consider a D-dimensional Gaussian random variable x with distribution N(x|,) in which the covariance matrix is known and for which we wish to infer the mean from a set of observations X = {x1, . . . , xN}. Find the ML estimate of . Given a prior distribution p() = N(|0,0), find the corresponding posterior distribution p(|X), and the MAP estimate of .