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### 218003114_2_720603014_2_HW_CH3-Γ€Β½οΏ½Γ€ΒΈοΏ½

Course: ELECTRONIC PC2010S, Spring 2010
School: Tsinghua University
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Word Count: 141

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. 1 (3.10 in the textbook) Suppose X = {x1 , x2 ,L , xN } is (i.i.d.) sampled from N ( , ) : tell 2 whether the maximum-likelihood estimators of and 2 are biased. 2. (3.3 in the textbook) Suppose X = {x1 , x2 ,L , xN } is (i.i.d.) sampled from: f ( x, P) = P xQ (1- x ) , x = 0,1, 0 P 1, Q = 1 - P . Show the maximum-likelihood estimator of P . 3. Show that if our model is poor, the maximum likelihood...

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. 1 (3.10 in the textbook) Suppose X = {x1 , x2 ,L , xN } is (i.i.d.) sampled from N ( , ) : tell 2 whether the maximum-likelihood estimators of and 2 are biased. 2. (3.3 in the textbook) Suppose X = {x1 , x2 ,L , xN } is (i.i.d.) sampled from: f ( x, P) = P xQ (1- x ) , x = 0,1, 0 P 1, Q = 1 - P . Show the maximum-likelihood estimator of P . 3. Show that if our model is poor, the maximum likelihood classifier we derive not is the best even among our poor model set by exploring the following examples. Suppose we have two equally probable categories (i.e., P (1 ) = P (2 ) = 0.5 ). Further, we know that p x|w ~N 0,1 but assume p x|w ~N , 1 . (That is , the parameter we seek by maximum likelihood techniques is the mean of the second distribution.) Imagine however that the true underlying distribution is p x|w ~N 1, 10 . 4.
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