Let X be an unobserved random variable with EX 0, Var(X) 5 Assume that we have observed Y 1 and Y 2 given by Y 1 2X W 1 , Y 2 X W 2 , where EW 1 EW 2 0, Var(W 1 ) 2, and Var(W 2 ) 5 Assume that W 1 , W 2 , and X are independent random variables Find the linear MMSE estimator of X, given Y 1 and Y 2

Question: Let X be an unobserved random variable with EX = 0, Var(X) = 5. Assume that we have observed Y 1 and Y 2 given

Let X be an unobserved random variable with EX = 0, Var(X) = 5. Assume that we have observed Y₁ and Y₂ given by

Y₁ = 2X +W₁,

Y₂ = X +W₂,

where EW₁ = EW₂ = 0, Var(W₁) = 2, and Var(W₂) = 5. Assume that W₁, W₂ , and X are independent random variables. Find the linear MMSE estimator of X, given Y₁ and Y₂.

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