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Quinta
2025-10-01 21:23:26 +02:00
commit 2653afd097
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.makemd/fileCache.mdc
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.makemd/superstate.mdc
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.obsidian/app.json
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{}
.obsidian/appearance.json
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{
"cssTheme": "Sanctum",
"theme": "moonstone",
"accentColor": "#89a4b3"
}
.obsidian/community-plugins.json
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[
"table-editor-obsidian",
"editing-toolbar",
"obsidian-excalidraw-plugin",
"image-converter",
"obsidian-latex-suite",
"make-md",
"obsidian-minimal-settings",
"obsidian-functionplot",
"omnisearch",
"obsidian-style-settings"
]
.obsidian/core-plugins.json
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{
"file-explorer": true,
"global-search": true,
"switcher": true,
"graph": true,
"backlink": true,
"canvas": true,
"outgoing-link": true,
"tag-pane": true,
"footnotes": false,
"properties": false,
"page-preview": true,
"daily-notes": true,
"templates": true,
"note-composer": true,
"command-palette": true,
"slash-command": false,
"editor-status": true,
"bookmarks": true,
"markdown-importer": false,
"zk-prefixer": false,
"random-note": false,
"outline": true,
"word-count": true,
"slides": false,
"audio-recorder": false,
"workspaces": false,
"file-recovery": true,
"publish": false,
"sync": true,
"bases": true,
"webviewer": false
}
.obsidian/graph.json
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{
"collapse-filter": true,
"search": "",
"showTags": false,
"showAttachments": false,
"hideUnresolved": false,
"showOrphans": true,
"collapse-color-groups": true,
"colorGroups": [],
"collapse-display": true,
"showArrow": false,
"textFadeMultiplier": 0,
"nodeSizeMultiplier": 1,
"lineSizeMultiplier": 1,
"collapse-forces": true,
"centerStrength": 0.518713248970312,
"repelStrength": 10,
"linkStrength": 1,
"linkDistance": 250,
"scale": 1,
"close": true
}
.obsidian/plugins/editing-toolbar/data.json
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{
"lastVersion": "3.1.18",
"aestheticStyle": "default",
"positionStyle": "top",
"menuCommands": [
{
"id": "editing-toolbar:editor-undo",
"name": "Undo editor",
"icon": "undo-glyph"
},
{
"id": "editing-toolbar:editor-redo",
"name": "Redo editor",
"icon": "redo-glyph"
},
{
"id": "editing-toolbar:toggle-format-brush",
"name": "Format Brush",
"icon": "paintbrush"
},
{
"id": "editing-toolbar:format-eraser",
"name": "Clear text formatting",
"icon": "eraser"
},
{
"id": "editing-toolbar:header2-text",
"name": "Header 2",
"icon": "header-2"
},
{
"id": "editing-toolbar:header3-text",
"name": "Header 3",
"icon": "header-3"
},
{
"id": "SubmenuCommands-header",
"name": "submenu",
"icon": "header-n",
"SubmenuCommands": [
{
"id": "editing-toolbar:header1-text",
"name": "Header 1",
"icon": "header-1"
},
{
"id": "editing-toolbar:header4-text",
"name": "Header 4",
"icon": "header-4"
},
{
"id": "editing-toolbar:header5-text",
"name": "Header 5",
"icon": "header-5"
},
{
"id": "editing-toolbar:header6-text",
"name": "Header 6",
"icon": "header-6"
}
]
},
{
"id": "editing-toolbar:toggle-bold",
"name": "Bold",
"icon": "bold-glyph"
},
{
"id": "editing-toolbar:toggle-italics",
"name": "Italics",
"icon": "italic-glyph"
},
{
"id": "editing-toolbar:toggle-strikethrough",
"name": "Strikethrough",
"icon": "strikethrough-glyph"
},
{
"id": "editing-toolbar:underline",
"name": "Underline",
"icon": "underline-glyph"
},
{
"id": "editing-toolbar:toggle-highlight",
"name": "==Highlight==",
"icon": "highlight-glyph"
},
{
"id": "SubmenuCommands-lucdf3en5",
"name": "submenu",
"icon": "edit",
"SubmenuCommands": [
{
"id": "editing-toolbar:editor-copy",
"name": "Copy",
"icon": "lucide-copy"
},
{
"id": "editing-toolbar:editor-cut",
"name": "Cut",
"icon": "lucide-scissors"
},
{
"id": "editing-toolbar:editor-paste",
"name": "Paste",
"icon": "lucide-clipboard-type"
},
{
"id": "editing-toolbar:editor:swap-line-down",
"name": "Swap line down",
"icon": "lucide-corner-right-down"
},
{
"id": "editing-toolbar:editor:swap-line-up",
"name": "Swap line up",
"icon": "lucide-corner-right-up"
}
]
},
{
"id": "editing-toolbar:editor:attach-file",
"name": "Attach file",
"icon": "lucide-paperclip"
},
{
"id": "editing-toolbar:editor:insert-table",
"name": "Insert Table",
"icon": "lucide-table"
},
{
"id": "editing-toolbar:editor:cycle-list-checklist",
"name": "Cycle list checklist",
"icon": "check-circle"
},
{
"id": "SubmenuCommands-luc8efull",
"name": "submenu",
"icon": "message-square",
"SubmenuCommands": [
{
"id": "editing-toolbar:editor:toggle-blockquote",
"name": "Blockquote",
"icon": "lucide-text-quote"
},
{
"id": "editing-toolbar:insert-callout",
"name": "Insert Callout ",
"icon": "lucide-quote"
}
]
},
{
"id": "SubmenuCommands-mdcmder",
"name": "submenu",
"icon": "<svg width=\"18\" height=\"18\" focusable=\"false\" fill=\"currentColor\" viewBox=\"0 0 1024 1024\"><g transform=\"scale(1, -1) translate(0, -896) scale(0.9, 0.9) \"><path class=\"path\" d=\"M464 608 l0 -568 q0 -3 -2.5 -5.5 q-2.5 -2.5 -5.5 -2.5 l-80 0 q-3 0 -5.5 2.5 q-2.5 2.5 -2.5 5.5 l0 568 l-232 0 q-3 0 -5.5 2.5 q-2.5 2.5 -2.5 5.5 l0 80 q0 3 2.5 5.5 q2.5 2.5 5.5 2.5 l560 0 q3 0 5.5 -2.5 q2.5 -2.5 2.5 -5.5 l0 -80 q0 -3 -2.5 -5.5 q-2.5 -2.5 -5.5 -2.5 l-232 0 ZM864 696 q17 0 28.5 11.5 q11.5 11.5 11.5 28.5 q0 17 -11.5 28.5 q-11.5 11.5 -28.5 11.5 q-17 0 -28.5 -11.5 q-11.5 -11.5 -11.5 -28.5 q0 -17 11.5 -28.5 q11.5 -11.5 28.5 -11.5 ZM864 640 q-40 0 -68 28 q-28 28 -28 68 q0 40 28 68 q28 28 68 28 q40 0 68 -28 q28 -28 28 -68 q0 -40 -28 -68 q-28 -28 -68 -28 ZM576 322 l0 -63 q0 -3 2 -5 l89 -70 l-89 -70 q-2 -2 -2 -5 l0 -63 q0 -4 3.5 -5.5 q3.5 -1.5 6.5 0.5 l170 133 q4 3 4.5 8.5 q0.5 5.5 -2.5 9.5 l-2 2 l-170 133 q-3 2 -6.5 0.5 q-3.5 -1.5 -3.5 -5.5 ZM256 322 l0 -63 q0 -3 -2 -5 l-89 -70 l89 -70 q2 -2 2 -5 l0 -63 q0 -4 -3.5 -5.5 q-3.5 -1.5 -6.5 0.5 l-170 133 q-4 3 -4.5 8.5 q-0.5 5.5 2.5 9.5 l2 2 l170 133 q3 2 6.5 0.5 q3.5 -1.5 3.5 -5.5 Z\"></path></g></svg>",
"SubmenuCommands": [
{
"id": "editing-toolbar:superscript",
"name": "Superscript",
"icon": "superscript-glyph"
},
{
"id": "editing-toolbar:subscript",
"name": "Subscript",
"icon": "subscript-glyph"
},
{
"id": "editing-toolbar:editor:toggle-code",
"name": "Inline code",
"icon": "code-glyph"
},
{
"id": "editing-toolbar:codeblock",
"name": "Code block",
"icon": "codeblock-glyph"
},
{
"id": "editing-toolbar:editor:insert-wikilink",
"name": "Insert wikilink [[]]",
"icon": "<svg width=\"15\" height=\"15\" focusable=\"false\" fill=\"currentColor\" viewBox=\"0 0 1024 1024\"><g transform=\"scale(1, -1) translate(0, -896) scale(0.9, 0.9) \"><path class=\"path\" d=\"M306 134 l91 0 q1 0 1 -8 l0 -80 q0 -8 -1 -8 l-91 0 q-1 0 -1 7 q0 -8 -5 -8 l-45 0 q-5 0 -5 8 l0 784 q0 8 5 8 l45 0 q5 0 5 -8 q0 8 1 8 l91 0 q1 0 1 -8 l0 -80 q0 -8 -1 -8 l-91 0 q-1 0 -1 8 l0 -623 q0 8 1 8 ZM139 134 l91 0 q1 0 1 -8 l0 -80 q0 -8 -1 -8 l-91 0 q-1 0 -1 7 q0 -8 -5 -8 l-45 0 q-5 0 -5 8 l0 784 q0 8 5 8 l45 0 q5 0 5 -8 q0 8 1 8 l91 0 q1 0 1 -8 l0 -80 q0 -8 -1 -8 l-91 0 q-1 0 -1 8 l0 -623 q0 8 1 8 ZM711 134 q1 0 1 -8 l0 623 q0 -8 -1 -8 l-91 0 q-1 0 -1 8 l0 80 q0 8 1 8 l91 0 q1 0 1 -8 q0 8 4 8 l46 0 q4 0 4 -8 l0 -784 q0 -8 -4 -8 l-46 0 q-4 0 -4 8 q0 -7 -1 -7 l-91 0 q-1 0 -1 8 l0 80 q0 8 1 8 l91 0 ZM878 134 q1 0 1 -8 l0 623 q0 -8 -1 -8 l-91 0 q-1 0 -1 8 l0 80 q0 8 1 8 l91 0 q1 0 1 -8 q0 8 5 8 l45 0 q4 0 4 -8 l0 -784 q0 -8 -4 -8 l-45 0 q-5 0 -5 8 q0 -7 -1 -7 l-91 0 q-1 0 -1 8 l0 80 q0 8 1 8 l91 0 Z\"></path></g></svg>"
},
{
"id": "editing-toolbar:editor:insert-embed",
"name": "Insert embed ![[]]",
"icon": "note-glyph"
},
{
"id": "editing-toolbar:insert-link",
"name": "Insert link []()",
"icon": "link-glyph"
},
{
"id": "editing-toolbar:hrline",
"name": "Horizontal divider",
"icon": "<svg width=\"18\" height=\"18\" focusable=\"false\" fill=\"currentColor\" viewBox=\"0 0 1024 1024\"><g transform=\"scale(1, -1) translate(0, -896) scale(0.9, 0.9) \"><path class=\"path\" d=\"M912 424 l0 -80 q0 -3 -2.5 -5.5 q-2.5 -2.5 -5.5 -2.5 l-784 0 q-3 0 -5.5 2.5 q-2.5 2.5 -2.5 5.5 l0 80 q0 3 2.5 5.5 q2.5 2.5 5.5 2.5 l784 0 q3 0 5.5 -2.5 q2.5 -2.5 2.5 -5.5 Z\"></path></g></svg>"
},
{
"id": "editing-toolbar:toggle-inline-math",
"name": "Inline math",
"icon": "lucide-sigma"
},
{
"id": "editing-toolbar:editor:insert-mathblock",
"name": "MathBlock",
"icon": "lucide-sigma-square"
}
]
},
{
"id": "SubmenuCommands-list",
"name": "submenu-list",
"icon": "bullet-list-glyph",
"SubmenuCommands": [
{
"id": "editing-toolbar:editor:toggle-checklist-status",
"name": "Checklist",
"icon": "checkbox-glyph"
},
{
"id": "editing-toolbar:renumber-ordered-list",
"name": "Renumber ordered list",
"icon": "list-restart"
},
{
"id": "editing-toolbar:toggle-numbered-list",
"name": "Numbered list",
"icon": "<svg width=\"18\" height=\"18\" focusable=\"false\" fill=\"currentColor\" viewBox=\"0 0 1024 1024\"><g transform=\"scale(1, -1) translate(0, -896) scale(0.9, 0.9) \"><path class=\"path\" d=\"M860 424 q17 0 28.5 -11.5 q11.5 -11.5 11.5 -28 q0 -16.5 -11.5 -28.5 q-11.5 -12 -27.5 -12 l-457 0 q-17 0 -28.5 11.5 q-11.5 11.5 -11.5 28 q0 16.5 11.5 28.5 q11.5 12 27.5 12 l457 0 ZM860 756 q17 0 28.5 -11.5 q11.5 -11.5 11.5 -28 q0 -16.5 -11.5 -28.5 q-11.5 -12 -27.5 -12 l-457 0 q-17 0 -28.5 11.5 q-11.5 11.5 -11.5 28 q0 16.5 11.5 28.5 q11.5 12 27.5 12 l457 0 ZM860 92 q17 0 28.5 -11.5 q11.5 -11.5 11.5 -28 q0 -16.5 -11.5 -28.5 q-11.5 -12 -27.5 -12 l-457 0 q-17 0 -28.5 11.5 q-11.5 11.5 -11.5 28 q0 16.5 11.5 28.5 q11.5 12 27.5 12 l457 0 ZM264 136 l-3 -3 l-51 -57 l56 0 q14 0 24.5 -10 q10.5 -10 11.5 -25 l0 -1 q0 -15 -10.5 -25.5 q-10.5 -10.5 -24.5 -10.5 l-137 0 q-15 0 -25 10 q-10 10 -11 24.5 q-1 14.5 9 25.5 l63 70 l49 54 q7 7 7 16.5 q0 9.5 -7.5 16.5 q-7.5 7 -18.5 7 q-11 0 -18.5 -6.5 q-7.5 -6.5 -8.5 -16.5 l0 0 q0 -15 -10.5 -25.5 q-10.5 -10.5 -25.5 -10.5 q-15 0 -25.5 10.5 q-10.5 10.5 -10.5 25.5 q0 26 13.5 47.5 q13.5 21.5 36 34.5 q22.5 13 49 13 q26.5 0 49.5 -13 q23 -13 36 -34.5 q13 -21.5 13 -47.5 q0 -20 -7.5 -37.5 q-7.5 -17.5 -21.5 -30.5 l-1 -1 ZM173 794 q11 11 25 10.5 q14 -0.5 24.5 -10.5 q10.5 -10 10.5 -25 l0 -293 q0 -15 -10 -25.5 q-10 -10.5 -25 -10.5 q-15 0 -25.5 10 q-10.5 10 -11.5 25 l0 211 q-10 -8 -23.5 -7 q-13.5 1 -22.5 11 l-1 0 q-10 11 -9.5 25.5 q0.5 14.5 10.5 24.5 l58 54 Z\"></path></g></svg>"
},
{
"id": "editing-toolbar:toggle-bullet-list",
"name": "Bullet list",
"icon": "<svg width=\"18\" height=\"18\" focusable=\"false\" fill=\"currentColor\" viewBox=\"0 0 1024 1024\"><g transform=\"scale(1, -1) translate(0, -896) scale(0.9, 0.9) \"><path class=\"path\" d=\"M860 424 q17 0 28.5 -11.5 q11.5 -11.5 11.5 -28 q0 -16.5 -11.5 -28.5 q-11.5 -12 -27.5 -12 l-477 0 q-17 0 -28.5 11.5 q-11.5 11.5 -11.5 28 q0 16.5 11.5 28.5 q11.5 12 27.5 12 l477 0 ZM860 756 q17 0 28.5 -11.5 q11.5 -11.5 11.5 -28 q0 -16.5 -11.5 -28.5 q-11.5 -12 -27.5 -12 l-477 0 q-17 0 -28.5 11.5 q-11.5 11.5 -11.5 28 q0 16.5 11.5 28.5 q11.5 12 27.5 12 l477 0 ZM860 92 q17 0 28.5 -11.5 q11.5 -11.5 11.5 -28 q0 -16.5 -11.5 -28.5 q-11.5 -12 -27.5 -12 l-477 0 q-17 0 -28.5 11.5 q-11.5 11.5 -11.5 28 q0 16.5 11.5 28.5 q11.5 12 27.5 12 l477 0 ZM176 716 l0 0 ZM112 716 q0 -27 18.5 -45.5 q18.5 -18.5 45.5 -18.5 q27 0 45.5 18.5 q18.5 18.5 18.5 45.5 q0 27 -18.5 45.5 q-18.5 18.5 -45.5 18.5 q-27 0 -45.5 -18.5 q-18.5 -18.5 -18.5 -45.5 ZM176 384 l0 0 ZM112 384 q0 -27 18.5 -45.5 q18.5 -18.5 45.5 -18.5 q27 0 45.5 18.5 q18.5 18.5 18.5 45.5 q0 27 -18.5 45.5 q-18.5 18.5 -45.5 18.5 q-27 0 -45.5 -18.5 q-18.5 -18.5 -18.5 -45.5 ZM176 52 l0 0 ZM112 52 q0 -27 18.5 -45.5 q18.5 -18.5 45.5 -18.5 q27 0 45.5 18.5 q18.5 18.5 18.5 45.5 q0 27 -18.5 45.5 q-18.5 18.5 -45.5 18.5 q-27 0 -45.5 -18.5 q-18.5 -18.5 -18.5 -45.5 Z\"></path></g></svg>"
},
{
"id": "editing-toolbar:undent-list",
"name": "Unindent-list",
"icon": "<svg width=\"18\" height=\"18\" focusable=\"false\" fill=\"currentColor\" viewBox=\"0 0 1024 1024\"><g transform=\"scale(1, -1) translate(0, -896) scale(0.9, 0.9) \"><path class=\"path\" d=\"M872 302 q17 0 28.5 -11.5 q11.5 -11.5 11.5 -28 q0 -16.5 -11.5 -28.5 q-11.5 -12 -27.5 -12 l-429 0 q-17 0 -28.5 11.5 q-11.5 11.5 -11.5 28 q0 16.5 11.5 28.5 q11.5 12 27.5 12 l429 0 ZM872 542 q17 0 28.5 -11.5 q11.5 -11.5 11.5 -28 q0 -16.5 -11.5 -28.5 q-11.5 -12 -27.5 -12 l-429 0 q-17 0 -28.5 11.5 q-11.5 11.5 -11.5 28 q0 16.5 11.5 28.5 q11.5 12 27.5 12 l429 0 ZM872 784 q17 0 28.5 -11.5 q11.5 -11.5 11.5 -28 q0 -16.5 -11.5 -28.5 q-11.5 -12 -27.5 -12 l-721 0 q-17 0 -28.5 11.5 q-11.5 11.5 -11.5 28 q0 16.5 11.5 28.5 q11.5 12 27.5 12 l721 0 ZM872 62 q17 0 28.5 -11.5 q11.5 -11.5 11.5 -28 q0 -16.5 -11.5 -28.5 q-11.5 -12 -27.5 -12 l-721 0 q-17 0 -28.5 11.5 q-11.5 11.5 -11.5 28 q0 16.5 11.5 28.5 q11.5 12 27.5 12 l721 0 ZM244 534 l-123 -122 q-8 -7 -8 -18 q0 -11 8 -18 l123 -122 q8 -7 19 -7 q11 0 18.5 7.5 q7.5 7.5 7.5 18.5 l0 242 q0 11 -7.5 18.5 q-7.5 7.5 -18.5 7.5 q-11 0 -19 -7 Z\"></path></g></svg>"
},
{
"id": "editing-toolbar:indent-list",
"name": "Indent list",
"icon": "<svg width=\"18\" height=\"18\" focusable=\"false\" fill=\"currentColor\" viewBox=\"0 0 1024 1024\"><g transform=\"scale(1, -1) translate(0, -896) scale(0.9, 0.9) \"><path class=\"path\" d=\"M872 302 q17 0 28.5 -11.5 q11.5 -11.5 11.5 -28 q0 -16.5 -11.5 -28.5 q-11.5 -12 -27.5 -12 l-429 0 q-17 0 -28.5 11.5 q-11.5 11.5 -11.5 28 q0 16.5 11.5 28.5 q11.5 12 27.5 12 l429 0 ZM872 542 q17 0 28.5 -11.5 q11.5 -11.5 11.5 -28 q0 -16.5 -11.5 -28.5 q-11.5 -12 -27.5 -12 l-429 0 q-17 0 -28.5 11.5 q-11.5 11.5 -11.5 28 q0 16.5 11.5 28.5 q11.5 12 27.5 12 l429 0 ZM872 784 q17 0 28.5 -11.5 q11.5 -11.5 11.5 -28 q0 -16.5 -11.5 -28.5 q-11.5 -12 -27.5 -12 l-721 0 q-17 0 -28.5 11.5 q-11.5 11.5 -11.5 28 q0 16.5 11.5 28.5 q11.5 12 27.5 12 l721 0 ZM872 62 q17 0 28.5 -11.5 q11.5 -11.5 11.5 -28 q0 -16.5 -11.5 -28.5 q-11.5 -12 -27.5 -12 l-721 0 q-17 0 -28.5 11.5 q-11.5 11.5 -11.5 28 q0 16.5 11.5 28.5 q11.5 12 27.5 12 l721 0 ZM158 534 l124 -122 q7 -7 7 -18 q0 -11 -7 -18 l-124 -122 q-7 -7 -18 -7 q-11 0 -19 7.5 q-8 7.5 -8 18.5 l0 242 q0 11 8 18.5 q8 7.5 19 7.5 q11 0 18 -7 Z\"></path></g></svg>"
}
]
},
{
"id": "SubmenuCommands-aligin",
"name": "submenu-aligin",
"icon": "<svg width=\"18\" height=\"18\" focusable=\"false\" fill=\"currentColor\" viewBox=\"0 0 1024 1024\"><g transform=\"scale(1, -1) translate(0, -896) scale(0.9, 0.9) \"><path class=\"path\" d=\"M724 304 q17 0 28.5 -11.5 q11.5 -11.5 11.5 -28 q0 -16.5 -11.5 -28.5 q-11.5 -12 -27.5 -12 l-421 0 q-17 0 -28.5 11.5 q-11.5 11.5 -11.5 28 q0 16.5 11.5 28.5 q11.5 12 27.5 12 l421 0 ZM872 540 q17 0 28.5 -11.5 q11.5 -11.5 11.5 -28 q0 -16.5 -11.5 -28.5 q-11.5 -12 -27.5 -12 l-721 0 q-17 0 -28.5 11.5 q-11.5 11.5 -11.5 28 q0 16.5 11.5 28.5 q11.5 12 27.5 12 l721 0 ZM724 776 q17 0 28.5 -11.5 q11.5 -11.5 11.5 -28 q0 -16.5 -11.5 -28.5 q-11.5 -12 -27.5 -12 l-421 0 q-17 0 -28.5 11.5 q-11.5 11.5 -11.5 28 q0 16.5 11.5 28.5 q11.5 12 27.5 12 l421 0 ZM872 68 q17 0 28.5 -11.5 q11.5 -11.5 11.5 -28 q0 -16.5 -11.5 -28.5 q-11.5 -12 -27.5 -12 l-721 0 q-17 0 -28.5 11.5 q-11.5 11.5 -11.5 28 q0 16.5 11.5 28.5 q11.5 12 27.5 12 l721 0 Z\"></path></g></svg>",
"SubmenuCommands": [
{
"id": "editing-toolbar:justify",
"name": "<p aligin=\"justify\"></p>",
"icon": "<svg width=\"18\" height=\"18\" focusable=\"false\" fill=\"currentColor\" viewBox=\"0 0 1024 1024\"><g transform=\"scale(1, -1) translate(0, -896) scale(0.9, 0.9) \"><path class=\"path\" d=\"M112 736 l0 0 ZM120 736 l784 0 q8 0 8 -8 l0 -80 q0 -8 -8 -8 l-784 0 q-8 0 -8 8 l0 80 q0 8 8 8 ZM112 331 l0 0 ZM120 331 l784 0 q8 0 8 -8 l0 -80 q0 -8 -8 -8 l-784 0 q-8 0 -8 8 l0 80 q0 8 8 8 ZM112 128 l0 0 ZM120 128 l784 0 q8 0 8 -8 l0 -80 q0 -8 -8 -8 l-784 0 q-8 0 -8 8 l0 80 q0 8 8 8 ZM112 533 l0 0 ZM120 533 l784 0 q8 0 8 -8 l0 -80 q0 -8 -8 -8 l-784 0 q-8 0 -8 8 l0 80 q0 8 8 8 Z\"></path></g></svg>"
},
{
"id": "editing-toolbar:left",
"name": "<p aligin=\"left\"></p>",
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/* Settings panel */
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*/
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span.cm-math.cm-concealed-mathrm, sub.cm-math.cm-concealed-mathrm {
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{
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This is your new *vault*.
Make a note of something, [[create a link]], or try [the Importer](https://help.obsidian.md/Plugins/Importer)!
When you're ready, delete this note and make the vault your own.
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# Ex 1
**Given data:** 4, 4, 7, 6, 6, 11, 1, 6, 3, 3 ($n = 10$ observations)
**True parameter:** $\lambda = 5$
### Part 1: Estimate the expected value of X
**Process:** For a Poisson distribution, E[X] = λ. We use the sample mean as an unbiased estimator.
**Solution:**
$$\bar{x}_n = \frac{1}{n}\sum_{i=1}^{n} x_i = \frac{4+4+7+6+6+11+1+6+3+3}{10} = \frac{51}{10} = 5.1$$
**Estimated $E[X] = 5.1$**
### Part 2: Estimate the variance using the unbiased estimator
**Process:** For Poisson distribution, $\text{Var}(X) = \lambda$. We use the corrected sample variance with $(n-1)$ denominator.
**Solution:**
First, calculate deviations from the mean:
- $(4-5.1)^2 = 1.21$
- $(4-5.1)^2 = 1.21$
- $(7-5.1)^2 = 3.61$
- $(6-5.1)^2 = 0.81$
- $(6-5.1)^2 = 0.81$
- $(11-5.1)^2 = 34.81$
- $(1-5.1)^2 = 16.81$
- $(6-5.1)^2 = 0.81$
- $(3-5.1)^2 = 4.41$
- $(3-5.1)^2 = 4.41$
$$S_n^2 = \frac{1}{n-1}\sum_{i=1}^{n}(x_i - \bar{x})^2 = \frac{1}{9} \times 68.9 = 7.66$$
**Estimated $\text{Var}(X) = 7.66$**
**Theory behind this:** $S_n^2 = \frac{1}{n-1}\sum_{i=1}^{n}(X_i - \bar{X}_n)^2$ is an unbiased estimator of $\text{Var}(X)$, while the version with denominator $n$ is biased. The $(n-1)$ correction accounts for the loss of one degree of freedom when estimating the mean.
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