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3 + X2
2 = 4
9 + E [X 2 ]
4 = 35
72 . MSE for L∗ (X ) = Thus,
Note that (MSE using g ∗ (X ) = 96 ) ≤ (MSE using L∗ =
are ordered in accordance with (4.36). 4.11 1
72 ) ≤ (Var(Y ) = 1
18 ), so the three MSEs Joint Gaussian distribution Recall that Gaussian distributions often arise in practice; this fact is explained by the CLT. The
CLT can be extended to two, or even more, correlated random variables. For example, suppose
(U1 , V1 ), (U2 , V2 ), · · · are independent, identically distributed pairs of random variables. For example, Ui might be the height, and Vi the weight, of the ith student to enroll at a university. Suppose
for convenience that they have mean zero. Then as n → ∞, the pair U1 +√n Un , V1 +√n Vn has a
limiting bivariate distribution, where “bivariate” means the limit distribution is a joint distribution
of two random variables. Suppose X and Y have such a limit distribution. Then X and Y must
each be Gaussian random var...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.
- Spring '08
- The Land