| { | |
| "markdown": "## ู ุจุฑููุฉ\nูุฃุญุฏ ุฃู ูุนุชุฑุถ ุนูู ูุฐุง ุจูููู ูู ูููุฉ ุงูุตููุงู : {ุฃูููุงู ุงู ู ูุนูุฏููุฏุงุชู} ุฃุฑุงุฏ ุจูุง\nP(A|B) = \\frac{P(A \\cap B)}{P(B)}\n## ุชุนุฑูู\nุงูุดูุฑ ููููุ ูุฃูู ุธุงูุฑ ููุธ ุงูุฃููุงู ู ู ุงูุซูุงุซุฉ ุฅูู ุงูุนุดุฑุฉ. ุฅูุงู ุฃูู ูุฏ ูุฐูุฑ ููุฑุงุฏ ุจู ุงูุฒูุงุฏุฉุ ููุฏ ูุณูุฑ ุงููู ุชุนุงูู ุฃูุงู ุงูุตูู ุจุงูุดููุฑุ ูุงูุนูุฏ ุจุฐูู ุงูุชูุณูุฑ. ูุฃู ุง ุฃูุงู ุงูุญูุถ\n\\mathbb{E}[x] = \\int x f_x(x) dx\n## ุจุฑูุงู\nูู ุจูู ุฉุ ููุง ุจุฏู ุฃู ุชููู ู ุญุตูุฑุฉุ ูุฃู ุงูุฃุญูุงู ุชุฎุชูู ุจุญุงู ุงูุญูุถ ูุงูุทููุฑุ ููุงู ุญู ู ุงูููุธ ุนูู ุธุงูุฑู ูุญูููุชู ุฃููู (1) .\n\\iint_{D} \\lambda^2 + j^2 \\, dx \\, dy", | |
| "images": [], | |
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| "hyperlinks": [], | |
| "header": null, | |
| "footer": null, | |
| "dimensions": { | |
| "dpi": 96, | |
| "height": 587, | |
| "width": 604 | |
| }, | |
| "confidence_scores": { | |
| "word_confidence_scores": [ | |
| { | |
| "text": "##", | |
| "confidence": 1.0, | |
| "start_index": 0 | |
| }, | |
| { | |
| "text": "ู ุจุฑููุฉ", | |
| "confidence": 1.0, | |
| "start_index": 3 | |
| }, | |
| { | |
| "text": "ูุฃุญุฏ", | |
| "confidence": 1.0, | |
| "start_index": 10 | |
| }, | |
| { | |
| "text": "ุฃู", | |
| "confidence": 1.0, | |
| "start_index": 15 | |
| }, | |
| { | |
| "text": "ูุนุชุฑุถ", | |
| "confidence": 1.0, | |
| "start_index": 18 | |
| }, | |
| { | |
| "text": "ุนูู", | |
| "confidence": 1.0, | |
| "start_index": 24 | |
| }, | |
| { | |
| "text": "ูุฐุง", | |
| "confidence": 1.0, | |
| "start_index": 28 | |
| }, | |
| { | |
| "text": "ุจูููู", | |
| "confidence": 1.0, | |
| "start_index": 32 | |
| }, | |
| { | |
| "text": "ูู", | |
| "confidence": 1.0, | |
| "start_index": 38 | |
| }, | |
| { | |
| "text": "ูููุฉ", | |
| "confidence": 1.0, | |
| "start_index": 41 | |
| }, | |
| { | |
| "text": "ุงูุตููุงู :", | |
| "confidence": 1.0, | |
| "start_index": 46 | |
| }, | |
| { | |
| "text": "{ุฃูููุงู ุงู", | |
| "confidence": 1.0, | |
| "start_index": 55 | |
| }, | |
| { | |
| "text": "ู ูุนูุฏููุฏุงุชู}", | |
| "confidence": 1.0, | |
| "start_index": 65 | |
| }, | |
| { | |
| "text": "ุฃุฑุงุฏ", | |
| "confidence": 1.0, | |
| "start_index": 78 | |
| }, | |
| { | |
| "text": "ุจูุง", | |
| "confidence": 1.0, | |
| "start_index": 83 | |
| }, | |
| { | |
| "text": "P(A|B)", | |
| "confidence": 1.0, | |
| "start_index": 87 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 94 | |
| }, | |
| { | |
| "text": "\\frac{P(A", | |
| "confidence": 1.0, | |
| "start_index": 96 | |
| }, | |
| { | |
| "text": "\\cap", | |
| "confidence": 1.0, | |
| "start_index": 106 | |
| }, | |
| { | |
| "text": "B)}{P(B)}", | |
| "confidence": 1.0, | |
| "start_index": 111 | |
| }, | |
| { | |
| "text": "##", | |
| "confidence": 1.0, | |
| "start_index": 121 | |
| }, | |
| { | |
| "text": "ุชุนุฑูู", | |
| "confidence": 1.0, | |
| "start_index": 124 | |
| }, | |
| { | |
| "text": "ุงูุดูุฑ", | |
| "confidence": 1.0, | |
| "start_index": 130 | |
| }, | |
| { | |
| "text": "ููููุ", | |
| "confidence": 1.0, | |
| "start_index": 136 | |
| }, | |
| { | |
| "text": "ูุฃูู", | |
| "confidence": 1.0, | |
| "start_index": 142 | |
| }, | |
| { | |
| "text": "ุธุงูุฑ", | |
| "confidence": 1.0, | |
| "start_index": 147 | |
| }, | |
| { | |
| "text": "ููุธ", | |
| "confidence": 1.0, | |
| "start_index": 152 | |
| }, | |
| { | |
| "text": "ุงูุฃููุงู ", | |
| "confidence": 1.0, | |
| "start_index": 156 | |
| }, | |
| { | |
| "text": "ู ู", | |
| "confidence": 1.0, | |
| "start_index": 164 | |
| }, | |
| { | |
| "text": "ุงูุซูุงุซุฉ", | |
| "confidence": 1.0, | |
| "start_index": 167 | |
| }, | |
| { | |
| "text": "ุฅูู", | |
| "confidence": 1.0, | |
| "start_index": 175 | |
| }, | |
| { | |
| "text": "ุงูุนุดุฑุฉ.", | |
| "confidence": 1.0, | |
| "start_index": 179 | |
| }, | |
| { | |
| "text": "ุฅูุงู", | |
| "confidence": 1.0, | |
| "start_index": 187 | |
| }, | |
| { | |
| "text": "ุฃูู", | |
| "confidence": 1.0, | |
| "start_index": 192 | |
| }, | |
| { | |
| "text": "ูุฏ", | |
| "confidence": 1.0, | |
| "start_index": 196 | |
| }, | |
| { | |
| "text": "ูุฐูุฑ", | |
| "confidence": 1.0, | |
| "start_index": 199 | |
| }, | |
| { | |
| "text": "ููุฑุงุฏ", | |
| "confidence": 1.0, | |
| "start_index": 204 | |
| }, | |
| { | |
| "text": "ุจู", | |
| "confidence": 1.0, | |
| "start_index": 210 | |
| }, | |
| { | |
| "text": "ุงูุฒูุงุฏุฉุ", | |
| "confidence": 1.0, | |
| "start_index": 213 | |
| }, | |
| { | |
| "text": "ููุฏ", | |
| "confidence": 1.0, | |
| "start_index": 222 | |
| }, | |
| { | |
| "text": "ูุณูุฑ", | |
| "confidence": 1.0, | |
| "start_index": 226 | |
| }, | |
| { | |
| "text": "ุงููู", | |
| "confidence": 1.0, | |
| "start_index": 231 | |
| }, | |
| { | |
| "text": "ุชุนุงูู", | |
| "confidence": 1.0, | |
| "start_index": 236 | |
| }, | |
| { | |
| "text": "ุฃูุงู ", | |
| "confidence": 1.0, | |
| "start_index": 242 | |
| }, | |
| { | |
| "text": "ุงูุตูู ", | |
| "confidence": 1.0, | |
| "start_index": 247 | |
| }, | |
| { | |
| "text": "ุจุงูุดููุฑุ", | |
| "confidence": 1.0, | |
| "start_index": 253 | |
| }, | |
| { | |
| "text": "ูุงูุนูุฏ", | |
| "confidence": 1.0, | |
| "start_index": 262 | |
| }, | |
| { | |
| "text": "ุจุฐูู", | |
| "confidence": 1.0, | |
| "start_index": 269 | |
| }, | |
| { | |
| "text": "ุงูุชูุณูุฑ.", | |
| "confidence": 1.0, | |
| "start_index": 274 | |
| }, | |
| { | |
| "text": "ูุฃู ุง", | |
| "confidence": 1.0, | |
| "start_index": 283 | |
| }, | |
| { | |
| "text": "ุฃูุงู ", | |
| "confidence": 1.0, | |
| "start_index": 288 | |
| }, | |
| { | |
| "text": "ุงูุญูุถ", | |
| "confidence": 1.0, | |
| "start_index": 293 | |
| }, | |
| { | |
| "text": "\\mathbb{E}[x]", | |
| "confidence": 1.0, | |
| "start_index": 299 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 313 | |
| }, | |
| { | |
| "text": "\\int", | |
| "confidence": 1.0, | |
| "start_index": 315 | |
| }, | |
| { | |
| "text": "x", | |
| "confidence": 1.0, | |
| "start_index": 320 | |
| }, | |
| { | |
| "text": "f_x(x)", | |
| "confidence": 1.0, | |
| "start_index": 322 | |
| }, | |
| { | |
| "text": "dx", | |
| "confidence": 1.0, | |
| "start_index": 329 | |
| }, | |
| { | |
| "text": "##", | |
| "confidence": 1.0, | |
| "start_index": 332 | |
| }, | |
| { | |
| "text": "ุจุฑูุงู", | |
| "confidence": 1.0, | |
| "start_index": 335 | |
| }, | |
| { | |
| "text": "ูู ุจูู ุฉุ", | |
| "confidence": 1.0, | |
| "start_index": 341 | |
| }, | |
| { | |
| "text": "ููุง", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ุจุฏู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ุฃู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ุชููู", | |
| "confidence": 1.0, | |
| "start_index": 360 | |
| }, | |
| { | |
| "text": "ู ุญุตูุฑุฉุ", | |
| "confidence": 1.0, | |
| "start_index": 365 | |
| }, | |
| { | |
| "text": "ูุฃู", | |
| "confidence": 1.0, | |
| "start_index": 373 | |
| }, | |
| { | |
| "text": "ุงูุฃุญูุงู ", | |
| "confidence": 1.0, | |
| "start_index": 377 | |
| }, | |
| { | |
| "text": "ุชุฎุชูู", | |
| "confidence": 1.0, | |
| "start_index": 385 | |
| }, | |
| { | |
| "text": "ุจุญุงู", | |
| "confidence": 1.0, | |
| "start_index": 391 | |
| }, | |
| { | |
| "text": "ุงูุญูุถ", | |
| "confidence": 1.0, | |
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| { | |
| "text": "ูุงูุทููุฑุ", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ููุงู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ุญู ู", | |
| "confidence": 1.0, | |
| "start_index": 416 | |
| }, | |
| { | |
| "text": "ุงูููุธ", | |
| "confidence": 1.0, | |
| "start_index": 420 | |
| }, | |
| { | |
| "text": "ุนูู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ุธุงูุฑู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ูุญูููุชู", | |
| "confidence": 1.0, | |
| "start_index": 436 | |
| }, | |
| { | |
| "text": "ุฃููู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "(1)", | |
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| { | |
| "text": ".", | |
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| }, | |
| { | |
| "text": "\\iint_{D}", | |
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| }, | |
| { | |
| "text": "\\lambda^2", | |
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| { | |
| "text": "+", | |
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| { | |
| "text": "j^2", | |
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| { | |
| "text": "\\,", | |
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| }, | |
| { | |
| "text": "dx", | |
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| }, | |
| { | |
| "text": "\\,", | |
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| }, | |
| { | |
| "text": "dy", | |
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| "content": "ู ุจุฑููุฉ", | |
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| "content": "ูุฃุญุฏ ุฃู ูุนุชุฑุถ ุนูู ูุฐุง ุจูููู ูู ูููุฉ ุงูุตููุงู : {ุฃูููุงู ุงู ู ูุนูุฏููุฏุงุชู} ุฃุฑุงุฏ ุจูุง", | |
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| "content": "P(A|B) = \\frac{P(A \\cap B)}{P(B)}", | |
| "type": "text", | |
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| "content": "ุชุนุฑูู", | |
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| "content": "ุงูุดูุฑ ููููุ ูุฃูู ุธุงูุฑ ููุธ ุงูุฃููุงู ู ู ุงูุซูุงุซุฉ ุฅูู ุงูุนุดุฑุฉ. ุฅูุงู ุฃูู ูุฏ ูุฐูุฑ ููุฑุงุฏ ุจู ุงูุฒูุงุฏุฉุ ููุฏ ูุณูุฑ ุงููู ุชุนุงูู ุฃูุงู ุงูุตูู ุจุงูุดููุฑุ ูุงูุนูุฏ ุจุฐูู ุงูุชูุณูุฑ. ูุฃู ุง ุฃูุงู ุงูุญูุถ", | |
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| "content": "\\mathbb{E}[x] = \\int x f_x(x) dx", | |
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| "top_left_x": 32, | |
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| "content": "ูู ุจูู ุฉุ ููุง ุจุฏู ุฃู ุชููู ู ุญุตูุฑุฉุ ูุฃู ุงูุฃุญูุงู ุชุฎุชูู ุจุญุงู ุงูุญูุถ ูุงูุทููุฑุ ููุงู ุญู ู ุงูููุธ ุนูู ุธุงูุฑู ูุญูููุชู ุฃููู (1) .", | |
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| { | |
| "top_left_x": 32, | |
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| "bottom_right_y": 515, | |
| "content": "\\iint_{D} \\lambda^2 + j^2 \\, dx \\, dy", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 9 | |
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| ], | |
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| "script": "arabic", | |
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