edits

Author: bmeyers

_posts/2024-11-18-Conditioning_joint_gaussian_on_sum.md

@@ -14,7 +14,7 @@ Let $X$ be a jointly Gaussian (j-g) random vector with mean $\mu\in\mathbf{R}^n$
 
 Because $S$ is a linear transform of j-g randon variables, $S$ is also itself Gaussian. As in the [prior post]({{ "/conditional_distribution_for_jointly_gaussian_random_vectors/" | absolute_url}}), we will exploit the unique property of Gaussians that uncorrelated variables are also independent.
 
-There is a Marimo notebook ([app](https://marimo.io/p/@gismo/notebook-mf27rb), [editable code](https://marimo.app/#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-nsdb7c7pEdSklSgHtfrkfHDqLAmr0T0ZCgqhEq09Q5HDajE9jBKJJLgSirHG6YRmO0ZHEyUSsgkSR4CkaTAXAYDqDAGIENYwpXNY6EcHQeCkEgYAzqsMSEeYyGINYSB9FcyEwJmtCmKoLDQMAODAAQJzarqCgGkan6mjR+R0Z4MSGAWkq-sSBCQSycQwRyaSAfGqx0WhGE5FccaYB0cinlum4AeukrYdYuH4TAhEzjpeBUCRZEsBRVG9LGIkwIx+YsLoYDdGQ5DcXqwB8Y6AlCXkIk4GJElXFJ-7WR0yyhBgzLRPJ7JwZyxHxjZdl3qpKGYcJKFPGQIDckmQU4DOwSfLs5isexnHqGFSHFeCeBlZ65CVfFtk1fIUBuMQhggDA5gAMK8IJ2wcXBo0TbwAgCH8OzfN5vkUC1bkecx3WIDggQnNYcAQCkOoiEF+qGiFkZxL8rnFaYcpBg99GReJP6EtJsmpWysHwVyiHaQleWtTAhV5JgAKrFDeAxAOoxNTgHB4GxdDVZKIntWVUMnLV3wNRxJwtbj6gwyIcMI0T6jI6jODo8DfWY21pUrtDA1DVAI1jSwk3TXAiNzTzk1LStXx7F5PmHuQW3FVo1htkxFgQDgsv0e5MBKwAomxhAAmcx2nQFvHXcaKB3WrHBPYQL3M29UWfX+MnJVBaX-ZlykCeBZIMsQr68mD9IUkcEPSnAHE5nD8DrdLCD4QQHDh-A1h0Ho6j+dYuggHA5QnU4eZQBTGcWkMunMJidzEBw+uOlWU6lvpy4ohS1cnGclZ3oORAfpe0aFi2CBTCI4KQtCMKepnZUoh0-XT7ZuJ2yVHXpOSldQK3gId2+3ejo2174xLhNNZb2MrzlB-mDHfl-Egg3DfNvNTSts3cwtouvVbeDPdFRXqzthgsBAPHf4UdoDWAxFnE6KQr4UDjgaOQABvCeWcz4zyyBwRYhgAC+lt3o-3xF9OKc87JJQiK7P6ikuQ8nyqhf4odWx4ShDnOgpB-jh2OsqawoBkJ4FNKsWoeBE4OAIAIIgOBSDAApkqUkk9jq514IvU+IgP4ayYgAl81ws6MCQdESez5sgYOwbgh2klCHOzIXJChGUlI0PUqHUy5kCLSFUMpUi0hyKaGcpbVRnlXSXgAsYj6pinY-WgulAGLj-Y0NDnTdmsTKbME9IjE4tM0YuI-qfWJJwVE7RYDrOUNdDYpCUIE-BBQzFwCyWTSpbEKYxFCW7Shu8vzhjvKHT03pfT+jzBQVQAAWRYP5Ax+mGIgcApgBydL9AGH0TQACsbBQJ72bDFCpqgpkgFGeMvAiUGlWIiZKYChzz4WlIMMAAjrAZYpywJNmuVcYh9yBirzRE8vI1DJLDM2dYMZPDrmhzACgaAmBurgmnJKB5ZzrCXJTHGIsc4NlbJ4cZK4VxSxnxbjXLe94d5e2-DCLI-sOAdEQKaYA1hsSSmCCi4SEBwQgvJfAZgo4LmwF6lQeFBQvlItMOuEsPsOgEqJSSslFLqVrmCdJJCdKDCgtoYC4AwK5V7IUtYqhAc1JISBVABl4IAUs2XsgsqCqlWMtWKS8ljBeD91osVHxzE1SQKNoQK0w4oFwAWdcX5pgilasVRMOVKB6iKqCB-PBjtvou0saqiJ1DpX0rle06ISBTTlSeCg3MsqzVKlFVawscBbyehABxNNejM26toRa6weaI0khVeEzKcbNXlsTZpX+S9Oq6IzTKit5rc3WpyZrTyjrs7OoIK631nqfnbN9Zm4g-quiMqDfoENJMdQ+l4OC1F+Qi2ktLd2hN2aq01oLZ3YtTQjWqBbUe-tNrt1wAADzMF4HgAQfSqW9nXeQRYA4gF7QvdEFoI5L3XvBH2y1A6ixPrLAADjmZKYA8Ev2bsDKkL9iw23bpEloUYZUBBbDgNaxe4bJV1qjb9GNmVQ7cOgPAW+qAlTHQyAh8AtHqxZzAFoRjd4WOQFgNcfCLh-yUWuOhXjbHLTIUcKMJwHBONSfgCJuipHSQZCiYHUT1h63uzSDyUOHJLSspTJaUOVwZTjT9GAFdBAcCLv2odUYdoJESnvZUwpqxRCgKgMdRJ0Rkk0xRmkkzEL8gyi1uhYkHFbPQt0MgR0UBXB0f8bwxlWnXOUQLvAVQog25uoAHzMAuBwE46gylYRhZgASchPMxHKN57FTwYXZcKZypJ1NkYcREM1rzGEQsEKdtcCrAkVNNyhTC3ZGBEOck4kA7ATBmAsGwEgDi2AWCYaVCyeEEkgA)) accompanying this post that allows you to play with some relevent numerical experiments. It runs in your browser, so feel free to edit and play around!
+There is a Marimo notebook ([app](https://marimo.io/p/@gismo/notebook-mf27rb), [editable code](https://marimo.app/#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-2V3ABHXonoyFBVCJVk9edF2bKMB1jAkiRJOAlFWON0wjPtoyOJkolZBIkjwFI0nguAwHUGAMQIaxhSuaxiI4Og8FIJAwA3VYYlo8x8MQawkD6K58JgTNaFMVQWGgYAcGAAgTm1XUFANI1QNNDj8i4zwYkMAtJUg4kCFQlk4gwjk0lg+NVi4oiSJyK440wDo5EfM9Txg49JXI6xKOomBaI3Cy8CoBimJYFi2N6WMFJgXj8xYXQwG6MhyHEvVgCkx0ZLkvIFJwJSVKuNToPcjpllCDBmWibT2Swzl6PjDyvK-QyCNI+SCKeMgQG5JM4pwDdgk+XZzEE4TRPUJK8Pq8E8Caz1yFa7LPI6+QoDcYhDBAGBzAAYV4WTthErDFpW3gBAEP4dm+cLIooAagpC-jxsQHBAhOaw4AgFIdREOL9UNBLIziX5Avq0w5SDH7uNS5SIMJdTNMKtlMOwrlcPMnKqsGmBaryTAAVWNG8BiWdRj6nAODwIS6HayUFOGpq0ZOTrvh6kSTgGyn1AxkQsZxun1HxwmcGJ+GptJobGoPdGZrmqAFqWlhVvWuBca2iXVr2g6vj2MKItvcgzvqrRrGHPiLAgHBNe44KYD1gBRITCABM57semLJPe40UC+o2OD+wgAf5oG0tBqCNPytCiuh0r9Jk5CyQZYhAN5JH6QpI4UelOARJzLH4GO9WEGoggOGT+BrDoPR1Gi6xdBAOBygepw8ygFmS4tIZLOYTE7mIDhrcdWs11Laz9xRCl25OM4ay-OciBA19o0LdsECmERwUhaEYU9UumpRDppvXzzcS9hqRvSclW6gQfARHoDx6XMCV2plXab613yYPiqb-MDOor+JBZvm7bJbWg7NvFjtRWgM3Z4H+ulOqxsLqGBYCAbO-w07QGsBiMuD0UhvwoFnA0cgADeK8y5Pw3lkcshgAC+rtgYQPxGDLKW8vJ5QiIHKGukuQ8mqoRf4ichxUShBXOgpB-jJ3usqawoB8J4FNKsWoeBc4OAIAIIgOBSDABZkqUkq97qV14LvR+IgQEmz4jAgC1wy6MDwdEVe-5sgkPISAyhvtwYBy0swkqel2HGUTo5ZyNFpCqH0oxaQzFND+VdgY0KrpXwwQoT7VSND-aMOcTpVxXJ9JsKRonLmwtMmsy7NEXGJxOZEz8SAx+mSTj6IuiwC2coO62xSEoaJINYl+zgGUpmrShIsxiBDdCxUYaXzfHgaOXDR7el9P6PMFBVAABZFgQUDH6YYiBwCmFnGMv0AYfRNArGwRCy42wZTifudZIAlkrKGQwgqvTg5pElPBO5z8LSkGGAAR1gMsJ5SFWwfKuHQn5AxD5on+XkNhqkFmnOsMs8RHzE5gBQNATA41wTrklL8551g3kpjjEWLcJyzniPslcK4pYn4Dw7mfb8F8w7gRhFkaOHAOiIFNMAaw2JJTBEJfJCA4JEUsvgMwXsrzYCTSoDigo4L8WmGPCWCOHRaX0sZcy1lHKjzNPUnhblBgkUcLhcABF2qelBxYc1dxeF4VQF5eCWFAt974Karq-VfLVhMpZYwXg09OL1TCfxNUqC7aECtAuNBcAdnXChaYOpZq9UTG1Sgeoeqgh2JiYcv2hqXH9LSUZDVPLtXWu4o-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-s5KJOB2AmDMBYNgJAIlsAsDE2heEKkgA)) accompanying this post that allows you to play with some relevent numerical experiments. It runs in your browser, so feel free to edit and play around!
 
 ### The Formula