diff --git a/articles/Determining Image Origin and Integrity Using Sensor Noise/Determining Image Origin and Integrity Using Sensor Noise.xopp.xml b/articles/Determining Image Origin and Integrity Using Sensor Noise/Determining Image Origin and Integrity Using Sensor Noise.xopp.xml
index 8785767..420d51c 100644
--- a/articles/Determining Image Origin and Integrity Using Sensor Noise/Determining Image Origin and Integrity Using Sensor Noise.xopp.xml	
+++ b/articles/Determining Image Origin and Integrity Using Sensor Noise/Determining Image Origin and Integrity Using Sensor Noise.xopp.xml	
@@ -505,6 +505,7 @@ interpolation step</text>
       <stroke tool="highlighter" color="#00c0ff7f" width="8.50000000" fill="128">202.09094238 520.32202148 202.09094238 566.10961914 251.14709473 566.10961914 251.14709473 520.32202148 202.09094238 520.32202148</stroke>
       <stroke tool="highlighter" color="#00c0ff7f" width="8.50000000" fill="128">282.03369141 541.94891357 282.03369141 541.94891357</stroke>
       <stroke tool="highlighter" color="#00c0ff7f" width="8.50000000" fill="128">99.37377930 736.74072266 176.71927425 736.74072266</stroke>
+      <stroke tool="pen" ts="0" fn="" color="#00c0ffff" width="1.41000000">288.54211426 625.82409668 332.89267338 791.34263666</stroke>
     </layer>
   </page>
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@@ -518,6 +519,7 @@ interpolation step</text>
       <teximage text="\iff \sum_{k=1}^N \frac{\mathbf{W}_k / \mathbf{I}_k}{1 / (\mathbf{I}_k)^2} = \mathbf{K} \sum_{k=1}^N \frac{1}{1 / (\mathbf{I}_k)^2}" left="142.56359863" top="106.72155762" right="302.95659863" bottom="147.87855762"/>
       <teximage text="\iff \mathbf{K} = \frac{\sum_{k=1}^N \frac{\mathbf{W}_k / \mathbf{I}_k}{1 / (\mathbf{I}_k)^2}}{\sum_{k=1}^N \frac{1}{1 / (\mathbf{I}_k)^2}}" left="142.22589111" top="148.70774841" right="258.83289111" bottom="191.65474841"/>
       <teximage text="\iff \mathbf{K} = \frac{\sum_{k=1}^N \mathbf{W}_k \mathbf{I}_k}{\sum_{k=1}^N (\mathbf{I}_k)^2}" left="142.66387939" top="187.59588623" right="256.17248725" bottom="225.59588623"/>
+      <teximage text="\text{by linearity of expected value, my actual question is why } \sum_{k=1}^NE[(\mathbf{I}_k)^2] = \sum_{k=1}^N(\mathbf{I}_k)^2?" left="311.52549129" top="-2.28384399" right="596.12817236" bottom="61.96316552"/>
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