update week 35
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@@ -2658,8 +2658,8 @@ If we then compute the expectation value (note the \( 1/n \) factor instead of \
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<p> <br>
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$$
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\mathbb{E}[\boldsymbol{X}^T\boldsymbol{X}] = \frac{1}{n}\boldsymbol{X}^T\boldsymbol{X}=\frac{1}{n}\begin{bmatrix}
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x_{00}^2+x_{01}^2 & x_{00}x_{10}+x_{01}x_{11}\\
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x_{10}x_{00}+x_{11}x_{01} & x_{10}^2+x_{11}^2\\
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x_{00}^2+x_{10}^2 & x_{00}x_{01}+x_{10}x_{11}\\
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x_{01}x_{00}+x_{11}x_{10} & x_{01}^2+x_{11}^2\\
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\end{bmatrix},
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$$
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<p> <br>
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@@ -2667,8 +2667,8 @@ $$
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If we then compute the expectation value (note the \( 1/n \) factor instead of \( 1/(n-1) \))
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$$
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\mathbb{E}[\boldsymbol{X}^T\boldsymbol{X}] = \frac{1}{n}\boldsymbol{X}^T\boldsymbol{X}=\frac{1}{n}\begin{bmatrix}
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x_{00}^2+x_{01}^2 & x_{00}x_{10}+x_{01}x_{11}\\
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x_{10}x_{00}+x_{11}x_{01} & x_{10}^2+x_{11}^2\\
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x_{00}^2+x_{10}^2 & x_{00}x_{01}+x_{10}x_{11}\\
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x_{01}x_{00}+x_{11}x_{10} & x_{01}^2+x_{11}^2\\
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\end{bmatrix},
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$$
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@@ -2672,8 +2672,8 @@ $$
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If we then compute the expectation value (note the \( 1/n \) factor instead of \( 1/(n-1) \))
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$$
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\mathbb{E}[\boldsymbol{X}^T\boldsymbol{X}] = \frac{1}{n}\boldsymbol{X}^T\boldsymbol{X}=\frac{1}{n}\begin{bmatrix}
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x_{00}^2+x_{01}^2 & x_{00}x_{10}+x_{01}x_{11}\\
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x_{10}x_{00}+x_{11}x_{01} & x_{10}^2+x_{11}^2\\
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x_{00}^2+x_{10}^2 & x_{00}x_{01}+x_{10}x_{11}\\
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x_{01}x_{00}+x_{11}x_{10} & x_{01}^2+x_{11}^2\\
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\end{bmatrix},
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$$
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Binary file not shown.
@@ -3411,8 +3411,8 @@
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"source": [
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"$$\n",
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"\\mathbb{E}[\\boldsymbol{X}^T\\boldsymbol{X}] = \\frac{1}{n}\\boldsymbol{X}^T\\boldsymbol{X}=\\frac{1}{n}\\begin{bmatrix}\n",
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"x_{00}^2+x_{01}^2 & x_{00}x_{10}+x_{01}x_{11}\\\\\n",
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"x_{10}x_{00}+x_{11}x_{01} & x_{10}^2+x_{11}^2\\\\\n",
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"x_{00}^2+x_{10}^2 & x_{00}x_{01}+x_{10}x_{11}\\\\\n",
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"x_{01}x_{00}+x_{11}x_{10} & x_{01}^2+x_{11}^2\\\\\n",
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"\\end{bmatrix},\n",
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"$$"
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]
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@@ -2151,8 +2151,8 @@ If we then compute the expectation value (note the $1/n$ factor instead of $1/(n
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!bt
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\[
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\mathbb{E}[\bm{X}^T\bm{X}] = \frac{1}{n}\bm{X}^T\bm{X}=\frac{1}{n}\begin{bmatrix}
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x_{00}^2+x_{01}^2 & x_{00}x_{10}+x_{01}x_{11}\\
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x_{10}x_{00}+x_{11}x_{01} & x_{10}^2+x_{11}^2\\
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x_{00}^2+x_{10}^2 & x_{00}x_{01}+x_{10}x_{11}\\
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x_{01}x_{00}+x_{11}x_{10} & x_{01}^2+x_{11}^2\\
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\end{bmatrix},
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\]
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!et
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