Assume you observe Y; where each Y; is independent and Gaussian with mean and variance given...

 

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Assume you observe Y; where each Y; is independent and Gaussian with mean and variance given by EY₂ = a₁: VarY₁ = alo², i=1...... (a) Estimate u and o2 using maximum likelihood assuming the vector a is known and all a, 7 0. (b) Assume you could choose to observe Y, for i = 1,...,n where EY₁ = ap; VarYao², i=1,...,n. assuming the vector a is known and all a, each Z, is independent and Gaussian with 0, or you could chose to observe Zi, i = 1,..., m where mean and constant variance given by EZ₁ = b;p: VarZ₁ = o², i=1,..., m. where b is known and all b, 0. Which sample should you prefer to acquire to estimate u and o²? Give your reasoning, and make assumptions about the magnitude of b Assume you observe Y; where each Y; is independent and Gaussian with mean and variance given by EY₂ = a₁: VarY₁ = alo², i=1...... (a) Estimate u and o2 using maximum likelihood assuming the vector a is known and all a, 7 0. (b) Assume you could choose to observe Y, for i = 1,...,n where EY₁ = ap; VarYao², i=1,...,n. assuming the vector a is known and all a, each Z, is independent and Gaussian with 0, or you could chose to observe Zi, i = 1,..., m where mean and constant variance given by EZ₁ = b;p: VarZ₁ = o², i=1,..., m. where b is known and all b, 0. Which sample should you prefer to acquire to estimate u and o²? Give your reasoning, and make assumptions about the magnitude of b

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a The maximum likelihood estimate of is given by 1n a where a is t... View the full answer