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{
"markdown": "## ู…ุจุฑู‡ู†ุฉ\nูˆุงู„ุนู…ู„ ูˆู‡ุฐุง ุงู„ู‚ูˆู„ ู„ุง ูŠู†ุงููŠ ุงู„ู‚ูˆู„ ุงู„ุฃูˆู„ ูุฅู† ู‡ุฐุง ุฅุฎุจุงุฑ ุนู† ูƒู„ ุงู„ุฃุนู…ุงู„ ุจุฃู†ู‡ุง ุจุงุทู„ุฉ ุฅู„ุง ู…ุง ุฃุฑูŠุฏ ุจู‡ ูˆุฌู‡ ุงู„ู„ู‡ ุชุนุงู„ู‰ ู…ู† ุงู„ุฃุนู…ุงู„ ุงู„ุตุงู„ุญุฉ ุงู„ู…ุทุงุจู‚ุฉ ู„ู„ุดุฑูŠุนุฉุŒ ูˆุงู„ู‚ูˆู„ ุงู„ุฃูˆู„ ู…ู‚ุชุถุงู‡ ุฃู† ูƒู„ ุงู„ุฐูˆุงุช ูุงู†ูŠุฉ ูˆุฒุงุฆู„ุฉ ุฅู„ุง ุฐุงุชู‡ ุชุนุงู„ู‰ ูˆุชู‚ุฏุณุŒ ูุฅู†ู‡ ุงู„ุฃูˆู„ ูˆุงู„ุขุฎุฑุŒ ุงู„ุฐูŠ ู‡ูˆ ู‚ุจู„ ูƒู„ ุดุฆ ูˆุจุนุฏ\n\\mathbb{E}[\\beta] = \\int x f_\\beta(x) dx\n\\sum_{i=0}^{N} \\frac{k^i}{i!} = e^{k} + \\frac{i}{\\lambda^2}\n\\sum_{\\alpha=0}^{N} \\frac{\\beta^\\alpha}{\\alpha!} = e^{\\beta} + \\frac{j}{\\beta^2}\n\\mathbb{E}[\\sigma] = \\int x f_\\sigma(x) dx + \\frac{y}{\\beta^2}\n## ุจุฑู‡ุงู†\nูƒู„ ุดุฆ. 2 - ูˆุจู…ู†ุงุณุจุฉ ู‚ูˆู„ู‡ ุชุนุงู„ู‰: ูƒูู„ู‘ู ุดูŽูŠู’ุกู ู‡ุงู„ููƒูŒ ุฅูู„ู‘ูŽุง ูˆูŽุฌู’ู‡ูŽู‡ู ุฐูƒุฑ ุงุจู† ูƒุซูŠุฑ ู…ุง ุฐูƒุฑู‡ ุงุจู† ุฃุจูŠ ุงู„ุฏู†ูŠุง ููŠ ูƒุชุงุจ (ุงู„ุชููƒุฑ ูˆุงู„ุงุนุชุจุงุฑ) ุจุณู†ุฏู‡ ุฅู„ู‰ ุงู„ูˆู„ูŠุฏ ู‚ุงู„: ูƒุงู† ุงุจู† ุนู…ุฑ ุฅุฐุง ุฃุฑุงุฏ ุฃู† ูŠุชุนุงู‡ุฏ\n\\sum_{j=0}^{100} \\frac{\\theta^j}{j!} = e^{\\theta} + \\frac{\\alpha}{i^2}\n## ู†ุธุฑูŠุฉ\nู‚ู„ุจู‡ ูŠุฃุชูŠ ุงู„ุฎุฑุจุฉุŒ ููŠู‚ู ุนู„ู‰ ุจุงุจู‡ุงุŒ ููŠู†ุงุฏูŠ ุจุตูˆุช ุญุฒูŠู† ููŠู‚ูˆู„: ุฃูŠู† ุฃู‡ู„ูƒุŸ ุซู… ูŠุฑุฌุน ุฅู„ู‰ ู†ูุณู‡ ููŠู‚ูˆู„: ูƒูู„ู‘ู ุดูŽูŠู’ุกู ู‡ุงู„ููƒูŒ ุฅูู„ู‘ูŽุง ูˆูŽุฌู’ู‡ูŽู‡ู. 3 - ูˆู†ุฎุชู… ุงู„ููˆุงุฆุฏ ุจุชุนู„ูŠู‚ุงุช\n\\beta_{n+1} = \\beta_n - \\alpha \\nabla f(\\beta_n) + \\frac{\\theta}{\\theta^2}\n\\iint_{D} x^2 \\leq \\lambda^2 \\, dx \\, dy\n\\mathbb{E}[\\lambda] = \\int x f_\\lambda(x) dx",
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