dataset / data /run_test_2_002 /annotations /sample_0000243.json
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"markdown": "ุงู„ูู„ุณูุฉ ุงู„ู…ุนุงุตุฑุฉ ูˆุฑุคูŠุชู‡ุง ู„ู„ูˆุงู‚ุน\n\\mathbb{E}[i] = \\int x f_i(x) dx\n\\int_{5}^{N} \\log(t) \\, dt = i^2 \\cdot C\nู…ู‚ุฏู…ุฉ ูˆุชู…ู‡ูŠุฏ ุนุงู…\nูุตู„ูˆุง ูˆู„ุง ูŠู‚ูˆู„ู‡ู† ุฃุญุฏูƒู…: ุฅู†ูŠ ู‚ุฏ ุตู„ูŠุช ูู„ุง ุฃุตู„ู‰\". \"ุนุจ\". 22500- \"ู…ุณู†ุฏ ุนุจุงุฏุฉ ุจู† ุงู„ุตุงู…ุช ุฑุถูŠ ุงู„ู„ู‡ ุนู†ู‡\" ูƒู†ุง ุฌู„ูˆุณุง ุนู†ุฏ ุฑุณูˆู„ ุงู„ู„ู‡ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ูู‚ุงู„: \"ุฅู†ู‡ุง ุณุชุฌูŠุก ุฃู…ุฑุงุก ุชุดุบู„ู‡ู… ุฃุดูŠุงุก ุญุชู‰ ู„ุง ูŠุตู„ูˆู† ุงู„ุตู„ุงุฉ ู„ู…ูŠู‚ุงุชู‡ุงุŒ ูุตู„ูˆุง ุงู„ุตู„ุงุฉ ู„ู…ูŠู‚ุงุชู‡ุง\" ูู‚ุงู„ ุฑุฌู„: \"ูŠุง ุฑุณูˆู„ ุงู„ู„ู‡ ุซู… ุฃุตู„ูŠ ู…ุนู‡ู…ุŸ \" ู‚ุงู„: \"ู†ุนู…\". \"ุนุจ\". 22501- ุนู† ุงุจู† ุนู…ุฑ ู‚ุงู„: \"ุฅู† ุงู„ุฑุฌู„ ู„ูŠุตู„ูŠ ุงู„ุตู„ุงุฉุŒ ูˆู„ู…ุง ูุงุชู‡ ู…ู† ูˆู‚ุชู‡ุง ุฎูŠุฑ ู„ู‡ ู…ู† ุฃู‡ู„ู‡ ูˆู…ุงู„ู‡\". \"ุต\". 22502- ุนู† ุนุจุฏ ุงู„ุฑุญู…ู† ุจู† ุงู„ุฃุณูˆุฏ ู‚ุงู„: \"ุงุณุชุฃุฐู† ุนู„ู‚ู…ุฉ ูˆุงู„ุฃุณูˆุฏ\n\\nabla_{\\mu} J(\\mu) = \\frac{1}{m} X^T ( \\sigma(X \\mu) - Y )\n\n![image](img-0)\n\nุงู„ุดูƒู„ (1): ุชุทูˆุฑ ู…ุคุดุฑุงุช ุงู„ุฃุฏุงุก ูˆุงู„ู…ุนุงูŠูŠุฑ ุงู„ู…ุนุชู…ุฏุฉ ุนุจุฑ ุงู„ุฒู…ู†\nุงู„ุฅุทุงุฑ ุงู„ู†ุธุฑูŠ ูˆุงู„ู…ูุงู‡ูŠู…ูŠ ู„ู„ุฏุฑุงุณุฉ\n253ุŒ 253ุŒ 255ุŒ 494 ุงู„ูˆู„ูŠุฏ ุจู† ูŠุฒูŠุฏ ุจู† ุนุจุฏ ุงู„ู…ู„ูƒ 375ุŒ 378 381ุŒ 384ุŒ 391ุŒ 393ุŒ 393ุŒ 394 ูˆู‡ุจ ุจู† ู…ู†ุจู‡ 286 ู‰ ูŠุฒูŠุฏ ุจู† ุนุจุฏ ุงู„ู…ู„ูƒ 337ุŒ 337ุŒ 338 393ุŒ 497 ูŠุฒูŠุฏ ุจู† ู…ุนุงูˆูŠุฉ 69ุŒ 75ุŒ 78ุŒ 85ุŒ 86ุŒ 492 ูŠุฒูŠุฏ ุจู† ุงู„ู…ู‡ู„ุจ 203ุŒ 204ุŒ 260 ูŠุฒูŠุฏ ุจู† ุงู„ูˆู„ูŠุฏ ุจู† ุนุจุฏ ุงู„ู…ู„ูƒ 97ุŒ 398 402ุŒ 498 ูŠูˆุณู ุจู† ุนู…ุฑ ุงู„ุซู‚ูู‰ 357ุŒ 359ุŒ 365 366ุŒ 473 ุชู… ูู‡ุฑุณ ุงู„ูƒุชุงุจ\nุงู„ู…ู‚ุงุฑุจุงุช ุงู„ู†ุธุฑูŠุฉ ูˆุงู„ู†ู…ุงุฐุฌ ุงู„ุชุญู„ูŠู„ูŠุฉ\n357ุŒ 359ุŒ 365 366ุŒ 473 ุชู… ูู‡ุฑุณ ุงู„ูƒุชุงุจ\nุงู„ุฑุคูŠุฉ ุงู„ู…ุณุชู‚ุจู„ูŠุฉ ูˆุฎุงุฑุทุฉ ุงู„ุทุฑูŠู‚\nุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ุฅู„ูŠู‡ู… ู„ูŠุตู„ุญ ุจูŠู†ู‡ู…ุŒ ูุฃุจุทุฃ ุนู„ู‰ ุงู„ู†ุงุณ\" ูู‚ุงู„ ุจู„ุงู„ ู„ุฃุจูŠ ุจูƒุฑ: \"ุฃู„ุง ุฃู‚ูŠู… ุงู„ุตู„ุงุฉุŸ \" ู‚ุงู„: \"ู…ุง ุดุฆุชุŒ ูุฃู‚ุงู… ุจู„ุงู„ ูู‚ุฏู… ุงู„ู†ุงุณ ุฃุจุง ุจูƒุฑ ูุจูŠู†ุง ู‡ูˆ ูŠุตู„ูŠ ุฃู‚ุจู„ ุงู„ู†ุจูŠ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ูุฌุนู„ ูŠุดู‚ ุงู„ุตููˆู ุญุชู‰ ู‚ุงู… ุฎู„ู ุฃุจูŠ ุจูƒุฑุŒ ูุฌุนู„ูˆุง ูŠุตูู‚ูˆู†ุŒ ูˆูƒุงู† ู„ุง ูŠู„ุชูุช ููŠ ุงู„ุตู„ุงุฉุŒ ูู„ู…ุง ุฃูƒุซุฑูˆุง ุงู„ุชูุชุŒ ูุฅุฐุง ุงู„ู†ุจูŠ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ู‚ุงุฆู… ุฎู„ูู‡ุŒ ูุฃุดุงุฑ ุฅู„ูŠู‡ ุงู„ู†ุจูŠ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ุฃู† ูŠุตู„ูŠ ูƒู…ุง ู‡ูˆ ูู†ูƒุต ุฅู„ู‰ ูˆุฑุงุฆู‡ุŒ ูˆุชู‚ุฏู… ุงู„ู†ุจูŠ\nุงู„ู…ุญุงูˆุฑ ูˆุงู„ุฃุจุนุงุฏ ุงู„ุฑุฆูŠุณูŠุฉ\nุจุงู„ูˆุทุก ูู„ุง ูŠุฑุฌุน ุจุจุฏู„ู‡ ุนู„ู‰ ุบูŠุฑู‡. ูˆู„ุง ูŠู‚ุงุณ ุนู„ู‰ ูˆู„ุฏ ุงู„ุฌุงุฑูŠุฉ ุงู„ู…ุณุชูˆู„ุฏุฉ. ูˆู„ูƒู† ุนู†ุฏ ุงุจู† ุฃุจูŠ ู„ูŠู„ู‰ ุฅู†ู‘ ุงู„ู…ุดุชุฑูŠ ูŠุฑุฌุน ุนู„ู‰ ุงู„ุจุงุฆุน ุจุงู„ุซู‘ู…ู† ูˆุจุงู„ู…ู‡ุฑ ูˆู‚ูŠู…ุฉ ุงู„ูˆู„ุฏ ุฎู„ุงูุงู‹ ู„ู„ุญู†ููŠู‘ุฉ ููŠ ุงู„ู…ู‡ุฑ. ูˆู…ู†ู‡ุง: ุฑุฌู„ ุชุณุญู‘ุฑ ููŠ ุดู‡ุฑ ุฑู…ุถุงู† ูˆู‚ุฏ ุทู„ุน ุงู„ูุฌุฑ - ูˆู‡ูˆ ู„ุง ูŠุนู„ู… ุจู‡ - ูุนู†ุฏ ุงู„ุญู†ููŠู‘ุฉ ูุณุฏ ุตูˆู…ู‡ุŒ ูˆุนู†ุฏ ุงุจู† ุฃุจูŠ ู„ูŠู„ู‰ ุตุญู‘ ุตูˆู…ู‡ ู‚ูŠุงุณุงู‹ ุนู„ู‰ ุงู„ู†ู‘ุงุณูŠ. ูˆุนู†ุฏ ุงู„ุญู†ููŠุฉ: ุฅู†ู‘ ุงู„ู…ุฎุทุฆ ู„ูŠุณ ูƒุงู„ู†ู‘ุงุณูŠุ› ู„ุฃู†ู‘\n## ุจุฑู‡ุงู†\n\\mathbb{E}[t] = \\int x f_t(x) dx\nุงู„ุฅุทุงุฑ ุงู„ู†ุธุฑูŠ ูˆุงู„ู…ูุงู‡ูŠู…ูŠ ู„ู„ุฏุฑุงุณุฉ\nู…ู†ู‡ุง ุดูŠุฆุง ุฃุฎุจุฑู†ุง ุฃุจูˆ ุงู„ู‚ุงุณู… ุงู„ุดุญุงู…ูŠ ุฃู†ุง ุฃุจูˆ ุณุนุฏ ุงู„ุฌู†ุฒุฑูˆุฏูŠ (6) ุฃู†ุง ุงู„ุญุงูƒู… ุฃุจูˆ ุฃุญู…ุฏ ุฃู†ุง ุฃุจูˆ ุฌุนูุฑ ู…ุญู…ุฏ ุจู† ุงู„ุญุณูŠู† ุงู„ุฎุซุนู…ูŠ ุจุงู„ูƒูˆูุฉ ู†ุง ุฌุนูุฑ ุจู† ู…ุญู…ุฏ ุจู† ุนุจุฏ ุงู„ุณู„ุงู… ู†ุง ุฃุจูˆ ู…ุนุงูˆูŠุฉ ุนู† ู…ูˆุณู‰ ุงู„ุตุบูŠุฑ ุนู† ุนุจุฏ ุงู„ุฑุญู…ู† ุจู† ุณุงุจุท ุนู† ุณุนูŠุฏ ุจู† ุญุฐูŠู… ู‚ุงู„\nP(A|B) = \\frac{P(A \\cap B)}{P(B)} + \\frac{j}{i^2}\nุชุญู„ูŠู„ ุงู„ู…ุชุบูŠุฑุงุช ูˆุงู„ุนูˆุงู…ู„ ุงู„ู…ุคุซุฑุฉ\nุฐู„ูƒ ุนู„ู‰ ู…ุง ูˆุฑุฏ ููŠู‡ ุงู„ู†ู‘ุตู‘. ูˆู…ู†ู‡ุง: ู†ุตู‘ ุงู„ุดู‘ุฑุน ุนู„ู‰ ุฃู†ู‘ ุงู„ุฅุฎูˆุฉ ู„ุฃู… ุฅุฐุง ูƒุงู†ูˆุง ุฐูƒูˆุฑุงู‹ ูˆุฅู†ุงุซุงู‹ ูู‡ู… ุดุฑูƒุงุก ููŠ ุงู„ุซู‘ู„ุซ. ูุฅุฐุง ู…ุงุช ุฑุฌู„ ูˆุชุฑูƒ ุงุจู†ุฉ ุฃุฎ ู„ุฃู…ู‘ ูˆุงุจู† ุฃุฎุช ู„ุฃู…ู‘ ูู‡ู„ ูŠู†ุฒู„ูˆู† ู…ู†ุฒู„ุฉ ุฃุตูˆู„ู‡ู… ุงู„ุชูŠ ุจู‡ุง ูŠุฏู„ูˆู†ุŸ ุฃูˆ ูŠู‚ุชุตุฑ ููŠ ุงู„ู†ู‘ุตู‘ ุนู„ู‰ ู…ูˆุฑุฏู‡ุŸ ููŠ ู‚ูˆู„ ุนู†ุฏ ุฃุจูŠ ูŠูˆุณู ุฑุญู…ู‡ ุงู„ู„ู‡ ูŠู‚ุชุตุฑ ููŠ ุงู„ู†ู‘ุตู‘ ุนู„ู‰ ู…ูˆุฑุฏู‡ุ› ู„ุฃู†ู‘ู‡ ู…ุฎุตูˆุต ู…ู† ุงู„ู‚ูŠุงุณ ุจุงู„ู†ู‘ุตู‘. ูˆุฃูˆู„ุงุฏ ุงู„ุฃุฎูˆุฉ ู„ุฃู…ู‘ ู„ูŠุณูˆุง ููŠ ู…ุนู†ู‰ ุงู„ุขุจุงุกุ› ู„ุฃู†ู‘ู‡ู… ู„ุง ูŠุฑุซูˆู† ุจุงู„ูุฑุถูŠู‘ุฉ ุดูŠุฆุงู‹. ูˆู…ู†ู‡ุง: ุฃู†ู‘ ุงู„ู…ุดุชุฑูŠ ู„ู„ุฌุงุฑูŠุฉ ุงู„ู…ุณุชุญู‚ู‘ุฉ ูŠุฑุฌุน ุนู„ู‰ ุงู„ุจุงุฆุน ุจุงู„ุซู‘ู…ู†ุŒ ูˆู„ูˆ ุงุณุชูˆู„ุฏู‡ุง ูŠุฑุฌุน ุนู„ู‰ ุงู„ุจุงุฆุน ุจู‚ูŠู…ุฉ ุงู„ูˆู„ุฏุŒ ูˆู‡ุฐุง ู‡ูˆ ุงู„ู…ุฎุตูˆุต ู…ู† ุงู„ู‚ูŠุงุณ ุจุงุชู‘ูุงู‚ ุงู„ุตู‘ุญุงุจุฉ. ู„ูƒู† ุฅุฐุง ูˆุทุฆ ุงู„ู…ุดุชุฑูŠ ุงู„ุฌุงุฑูŠุฉ ููŠุฌุจ ุนู„ูŠู‡ ู…ู‡ุฑู‡ุง ู„ู…ุณุชุญู‚ู‘ู‡ุงุŒ ูˆูŠู‚ุถู‰ ุจู‡ุง ู„ู…ุณุชุญู‚ู‘ู‡ุง",
"images": [
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"hyperlinks": [],
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"confidence_scores": {
"word_confidence_scores": [
{
"text": "ุงู„ูู„ุณูุฉ",
"confidence": 1.0,
"start_index": 0
},
{
"text": "ุงู„ู…ุนุงุตุฑุฉ",
"confidence": 1.0,
"start_index": 8
},
{
"text": "ูˆุฑุคูŠุชู‡ุง",
"confidence": 1.0,
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"content": "ูุตู„ูˆุง ูˆู„ุง ูŠู‚ูˆู„ู‡ู† ุฃุญุฏูƒู…: ุฅู†ูŠ ู‚ุฏ ุตู„ูŠุช ูู„ุง ุฃุตู„ู‰\". \"ุนุจ\". 22500- \"ู…ุณู†ุฏ ุนุจุงุฏุฉ ุจู† ุงู„ุตุงู…ุช ุฑุถูŠ ุงู„ู„ู‡ ุนู†ู‡\" ูƒู†ุง ุฌู„ูˆุณุง ุนู†ุฏ ุฑุณูˆู„ ุงู„ู„ู‡ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ูู‚ุงู„: \"ุฅู†ู‡ุง ุณุชุฌูŠุก ุฃู…ุฑุงุก ุชุดุบู„ู‡ู… ุฃุดูŠุงุก ุญุชู‰ ู„ุง ูŠุตู„ูˆู† ุงู„ุตู„ุงุฉ ู„ู…ูŠู‚ุงุชู‡ุงุŒ ูุตู„ูˆุง ุงู„ุตู„ุงุฉ ู„ู…ูŠู‚ุงุชู‡ุง\" ูู‚ุงู„ ุฑุฌู„: \"ูŠุง ุฑุณูˆู„ ุงู„ู„ู‡ ุซู… ุฃุตู„ูŠ ู…ุนู‡ู…ุŸ \" ู‚ุงู„: \"ู†ุนู…\". \"ุนุจ\". 22501- ุนู† ุงุจู† ุนู…ุฑ ู‚ุงู„: \"ุฅู† ุงู„ุฑุฌู„ ู„ูŠุตู„ูŠ ุงู„ุตู„ุงุฉุŒ ูˆู„ู…ุง ูุงุชู‡ ู…ู† ูˆู‚ุชู‡ุง ุฎูŠุฑ ู„ู‡ ู…ู† ุฃู‡ู„ู‡ ูˆู…ุงู„ู‡\". \"ุต\". 22502- ุนู† ุนุจุฏ ุงู„ุฑุญู…ู† ุจู† ุงู„ุฃุณูˆุฏ ู‚ุงู„: \"ุงุณุชุฃุฐู† ุนู„ู‚ู…ุฉ ูˆุงู„ุฃุณูˆุฏ",
"type": "text",
"confidence_scores": null,
"reading_index": 5
},
{
"top_left_x": 462,
"top_left_y": 455,
"bottom_right_x": 828,
"bottom_right_y": 506,
"content": "\\nabla_{\\mu} J(\\mu) = \\frac{1}{m} X^T ( \\sigma(X \\mu) - Y )",
"type": "text",
"confidence_scores": null,
"reading_index": 6
},
{
"top_left_x": 450,
"top_left_y": 541,
"bottom_right_x": 844,
"bottom_right_y": 805,
"content": "![image](img-0)",
"type": "image",
"confidence_scores": null,
"reading_index": 7
},
{
"top_left_x": 450,
"top_left_y": 811,
"bottom_right_x": 844,
"bottom_right_y": 832,
"content": "ุงู„ุดูƒู„ (1): ุชุทูˆุฑ ู…ุคุดุฑุงุช ุงู„ุฃุฏุงุก ูˆุงู„ู…ุนุงูŠูŠุฑ ุงู„ู…ุนุชู…ุฏุฉ ุนุจุฑ ุงู„ุฒู…ู†",
"type": "text",
"confidence_scores": null,
"reading_index": 8
},
{
"top_left_x": 450,
"top_left_y": 858,
"bottom_right_x": 844,
"bottom_right_y": 877,
"content": "ุงู„ุฅุทุงุฑ ุงู„ู†ุธุฑูŠ ูˆุงู„ู…ูุงู‡ูŠู…ูŠ ู„ู„ุฏุฑุงุณุฉ",
"type": "text",
"confidence_scores": null,
"reading_index": 9
},
{
"top_left_x": 450,
"top_left_y": 885,
"bottom_right_x": 844,
"bottom_right_y": 1011,
"content": "253ุŒ 253ุŒ 255ุŒ 494 ุงู„ูˆู„ูŠุฏ ุจู† ูŠุฒูŠุฏ ุจู† ุนุจุฏ ุงู„ู…ู„ูƒ 375ุŒ 378 381ุŒ 384ุŒ 391ุŒ 393ุŒ 393ุŒ 394 ูˆู‡ุจ ุจู† ู…ู†ุจู‡ 286 ู‰ ูŠุฒูŠุฏ ุจู† ุนุจุฏ ุงู„ู…ู„ูƒ 337ุŒ 337ุŒ 338 393ุŒ 497 ูŠุฒูŠุฏ ุจู† ู…ุนุงูˆูŠุฉ 69ุŒ 75ุŒ 78ุŒ 85ุŒ 86ุŒ 492 ูŠุฒูŠุฏ ุจู† ุงู„ู…ู‡ู„ุจ 203ุŒ 204ุŒ 260 ูŠุฒูŠุฏ ุจู† ุงู„ูˆู„ูŠุฏ ุจู† ุนุจุฏ ุงู„ู…ู„ูƒ 97ุŒ 398 402ุŒ 498 ูŠูˆุณู ุจู† ุนู…ุฑ ุงู„ุซู‚ูู‰ 357ุŒ 359ุŒ 365 366ุŒ 473 ุชู… ูู‡ุฑุณ ุงู„ูƒุชุงุจ",
"type": "text",
"confidence_scores": null,
"reading_index": 10
},
{
"top_left_x": 30,
"top_left_y": 95,
"bottom_right_x": 424,
"bottom_right_y": 117,
"content": "ุงู„ู…ู‚ุงุฑุจุงุช ุงู„ู†ุธุฑูŠุฉ ูˆุงู„ู†ู…ุงุฐุฌ ุงู„ุชุญู„ูŠู„ูŠุฉ",
"type": "text",
"confidence_scores": null,
"reading_index": 11
},
{
"top_left_x": 30,
"top_left_y": 125,
"bottom_right_x": 424,
"bottom_right_y": 150,
"content": "357ุŒ 359ุŒ 365 366ุŒ 473 ุชู… ูู‡ุฑุณ ุงู„ูƒุชุงุจ",
"type": "text",
"confidence_scores": null,
"reading_index": 12
},
{
"top_left_x": 30,
"top_left_y": 166,
"bottom_right_x": 424,
"bottom_right_y": 185,
"content": "ุงู„ุฑุคูŠุฉ ุงู„ู…ุณุชู‚ุจู„ูŠุฉ ูˆุฎุงุฑุทุฉ ุงู„ุทุฑูŠู‚",
"type": "text",
"confidence_scores": null,
"reading_index": 13
},
{
"top_left_x": 30,
"top_left_y": 193,
"bottom_right_x": 424,
"bottom_right_y": 319,
"content": "ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ุฅู„ูŠู‡ู… ู„ูŠุตู„ุญ ุจูŠู†ู‡ู…ุŒ ูุฃุจุทุฃ ุนู„ู‰ ุงู„ู†ุงุณ\" ูู‚ุงู„ ุจู„ุงู„ ู„ุฃุจูŠ ุจูƒุฑ: \"ุฃู„ุง ุฃู‚ูŠู… ุงู„ุตู„ุงุฉุŸ \" ู‚ุงู„: \"ู…ุง ุดุฆุชุŒ ูุฃู‚ุงู… ุจู„ุงู„ ูู‚ุฏู… ุงู„ู†ุงุณ ุฃุจุง ุจูƒุฑ ูุจูŠู†ุง ู‡ูˆ ูŠุตู„ูŠ ุฃู‚ุจู„ ุงู„ู†ุจูŠ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ูุฌุนู„ ูŠุดู‚ ุงู„ุตููˆู ุญุชู‰ ู‚ุงู… ุฎู„ู ุฃุจูŠ ุจูƒุฑุŒ ูุฌุนู„ูˆุง ูŠุตูู‚ูˆู†ุŒ ูˆูƒุงู† ู„ุง ูŠู„ุชูุช ููŠ ุงู„ุตู„ุงุฉุŒ ูู„ู…ุง ุฃูƒุซุฑูˆุง ุงู„ุชูุชุŒ ูุฅุฐุง ุงู„ู†ุจูŠ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ู‚ุงุฆู… ุฎู„ูู‡ุŒ ูุฃุดุงุฑ ุฅู„ูŠู‡ ุงู„ู†ุจูŠ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ุฃู† ูŠุตู„ูŠ ูƒู…ุง ู‡ูˆ ูู†ูƒุต ุฅู„ู‰ ูˆุฑุงุฆู‡ุŒ ูˆุชู‚ุฏู… ุงู„ู†ุจูŠ",
"type": "text",
"confidence_scores": null,
"reading_index": 14
},
{
"top_left_x": 30,
"top_left_y": 335,
"bottom_right_x": 424,
"bottom_right_y": 357,
"content": "ุงู„ู…ุญุงูˆุฑ ูˆุงู„ุฃุจุนุงุฏ ุงู„ุฑุฆูŠุณูŠุฉ",
"type": "text",
"confidence_scores": null,
"reading_index": 15
},
{
"top_left_x": 30,
"top_left_y": 365,
"bottom_right_x": 424,
"bottom_right_y": 466,
"content": "ุจุงู„ูˆุทุก ูู„ุง ูŠุฑุฌุน ุจุจุฏู„ู‡ ุนู„ู‰ ุบูŠุฑู‡. ูˆู„ุง ูŠู‚ุงุณ ุนู„ู‰ ูˆู„ุฏ ุงู„ุฌุงุฑูŠุฉ ุงู„ู…ุณุชูˆู„ุฏุฉ. ูˆู„ูƒู† ุนู†ุฏ ุงุจู† ุฃุจูŠ ู„ูŠู„ู‰ ุฅู†ู‘ ุงู„ู…ุดุชุฑูŠ ูŠุฑุฌุน ุนู„ู‰ ุงู„ุจุงุฆุน ุจุงู„ุซู‘ู…ู† ูˆุจุงู„ู…ู‡ุฑ ูˆู‚ูŠู…ุฉ ุงู„ูˆู„ุฏ ุฎู„ุงูุงู‹ ู„ู„ุญู†ููŠู‘ุฉ ููŠ ุงู„ู…ู‡ุฑ. ูˆู…ู†ู‡ุง: ุฑุฌู„ ุชุณุญู‘ุฑ ููŠ ุดู‡ุฑ ุฑู…ุถุงู† ูˆู‚ุฏ ุทู„ุน ุงู„ูุฌุฑ - ูˆู‡ูˆ ู„ุง ูŠุนู„ู… ุจู‡ - ูุนู†ุฏ ุงู„ุญู†ููŠู‘ุฉ ูุณุฏ ุตูˆู…ู‡ุŒ ูˆุนู†ุฏ ุงุจู† ุฃุจูŠ ู„ูŠู„ู‰ ุตุญู‘ ุตูˆู…ู‡ ู‚ูŠุงุณุงู‹ ุนู„ู‰ ุงู„ู†ู‘ุงุณูŠ. ูˆุนู†ุฏ ุงู„ุญู†ููŠุฉ: ุฅู†ู‘ ุงู„ู…ุฎุทุฆ ู„ูŠุณ ูƒุงู„ู†ู‘ุงุณูŠุ› ู„ุฃู†ู‘",
"type": "text",
"confidence_scores": null,
"reading_index": 16
},
{
"top_left_x": 42,
"top_left_y": 494,
"bottom_right_x": 408,
"bottom_right_y": 518,
"content": "ุจุฑู‡ุงู†",
"type": "title",
"confidence_scores": null,
"reading_index": 17
},
{
"top_left_x": 42,
"top_left_y": 524,
"bottom_right_x": 408,
"bottom_right_y": 578,
"content": "\\mathbb{E}[t] = \\int x f_t(x) dx",
"type": "text",
"confidence_scores": null,
"reading_index": 18
},
{
"top_left_x": 30,
"top_left_y": 626,
"bottom_right_x": 424,
"bottom_right_y": 648,
"content": "ุงู„ุฅุทุงุฑ ุงู„ู†ุธุฑูŠ ูˆุงู„ู…ูุงู‡ูŠู…ูŠ ู„ู„ุฏุฑุงุณุฉ",
"type": "text",
"confidence_scores": null,
"reading_index": 19
},
{
"top_left_x": 30,
"top_left_y": 656,
"bottom_right_x": 424,
"bottom_right_y": 731,
"content": "ู…ู†ู‡ุง ุดูŠุฆุง ุฃุฎุจุฑู†ุง ุฃุจูˆ ุงู„ู‚ุงุณู… ุงู„ุดุญุงู…ูŠ ุฃู†ุง ุฃุจูˆ ุณุนุฏ ุงู„ุฌู†ุฒุฑูˆุฏูŠ (6) ุฃู†ุง ุงู„ุญุงูƒู… ุฃุจูˆ ุฃุญู…ุฏ ุฃู†ุง ุฃุจูˆ ุฌุนูุฑ ู…ุญู…ุฏ ุจู† ุงู„ุญุณูŠู† ุงู„ุฎุซุนู…ูŠ ุจุงู„ูƒูˆูุฉ ู†ุง ุฌุนูุฑ ุจู† ู…ุญู…ุฏ ุจู† ุนุจุฏ ุงู„ุณู„ุงู… ู†ุง ุฃุจูˆ ู…ุนุงูˆูŠุฉ ุนู† ู…ูˆุณู‰ ุงู„ุตุบูŠุฑ ุนู† ุนุจุฏ ุงู„ุฑุญู…ู† ุจู† ุณุงุจุท ุนู† ุณุนูŠุฏ ุจู† ุญุฐูŠู… ู‚ุงู„",
"type": "text",
"confidence_scores": null,
"reading_index": 20
},
{
"top_left_x": 30,
"top_left_y": 753,
"bottom_right_x": 424,
"bottom_right_y": 793,
"content": "P(A|B) = \\frac{P(A \\cap B)}{P(B)} + \\frac{j}{i^2}",
"type": "text",
"confidence_scores": null,
"reading_index": 21
},
{
"top_left_x": 30,
"top_left_y": 799,
"bottom_right_x": 424,
"bottom_right_y": 818,
"content": "ุชุญู„ูŠู„ ุงู„ู…ุชุบูŠุฑุงุช ูˆุงู„ุนูˆุงู…ู„ ุงู„ู…ุคุซุฑุฉ",
"type": "text",
"confidence_scores": null,
"reading_index": 22
},
{
"top_left_x": 30,
"top_left_y": 826,
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"content": "ุฐู„ูƒ ุนู„ู‰ ู…ุง ูˆุฑุฏ ููŠู‡ ุงู„ู†ู‘ุตู‘. ูˆู…ู†ู‡ุง: ู†ุตู‘ ุงู„ุดู‘ุฑุน ุนู„ู‰ ุฃู†ู‘ ุงู„ุฅุฎูˆุฉ ู„ุฃู… ุฅุฐุง ูƒุงู†ูˆุง ุฐูƒูˆุฑุงู‹ ูˆุฅู†ุงุซุงู‹ ูู‡ู… ุดุฑูƒุงุก ููŠ ุงู„ุซู‘ู„ุซ. ูุฅุฐุง ู…ุงุช ุฑุฌู„ ูˆุชุฑูƒ ุงุจู†ุฉ ุฃุฎ ู„ุฃู…ู‘ ูˆุงุจู† ุฃุฎุช ู„ุฃู…ู‘ ูู‡ู„ ูŠู†ุฒู„ูˆู† ู…ู†ุฒู„ุฉ ุฃุตูˆู„ู‡ู… ุงู„ุชูŠ ุจู‡ุง ูŠุฏู„ูˆู†ุŸ ุฃูˆ ูŠู‚ุชุตุฑ ููŠ ุงู„ู†ู‘ุตู‘ ุนู„ู‰ ู…ูˆุฑุฏู‡ุŸ ููŠ ู‚ูˆู„ ุนู†ุฏ ุฃุจูŠ ูŠูˆุณู ุฑุญู…ู‡ ุงู„ู„ู‡ ูŠู‚ุชุตุฑ ููŠ ุงู„ู†ู‘ุตู‘ ุนู„ู‰ ู…ูˆุฑุฏู‡ุ› ู„ุฃู†ู‘ู‡ ู…ุฎุตูˆุต ู…ู† ุงู„ู‚ูŠุงุณ ุจุงู„ู†ู‘ุตู‘. ูˆุฃูˆู„ุงุฏ ุงู„ุฃุฎูˆุฉ ู„ุฃู…ู‘ ู„ูŠุณูˆุง ููŠ ู…ุนู†ู‰ ุงู„ุขุจุงุกุ› ู„ุฃู†ู‘ู‡ู… ู„ุง ูŠุฑุซูˆู† ุจุงู„ูุฑุถูŠู‘ุฉ ุดูŠุฆุงู‹. ูˆู…ู†ู‡ุง: ุฃู†ู‘ ุงู„ู…ุดุชุฑูŠ ู„ู„ุฌุงุฑูŠุฉ ุงู„ู…ุณุชุญู‚ู‘ุฉ ูŠุฑุฌุน ุนู„ู‰ ุงู„ุจุงุฆุน ุจุงู„ุซู‘ู…ู†ุŒ ูˆู„ูˆ ุงุณุชูˆู„ุฏู‡ุง ูŠุฑุฌุน ุนู„ู‰ ุงู„ุจุงุฆุน ุจู‚ูŠู…ุฉ ุงู„ูˆู„ุฏุŒ ูˆู‡ุฐุง ู‡ูˆ ุงู„ู…ุฎุตูˆุต ู…ู† ุงู„ู‚ูŠุงุณ ุจุงุชู‘ูุงู‚ ุงู„ุตู‘ุญุงุจุฉ. ู„ูƒู† ุฅุฐุง ูˆุทุฆ ุงู„ู…ุดุชุฑูŠ ุงู„ุฌุงุฑูŠุฉ ููŠุฌุจ ุนู„ูŠู‡ ู…ู‡ุฑู‡ุง ู„ู…ุณุชุญู‚ู‘ู‡ุงุŒ ูˆูŠู‚ุถู‰ ุจู‡ุง ู„ู…ุณุชุญู‚ู‘ู‡ุง",
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