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elizavetasemenova committed Nov 29, 2024
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":class: tip\n",
"Consider the coin flipping problem with probability of heads ('success') being modelled as $\\theta$. The experiment was repeated $n$ times, and we observed $h$ 'sucesses'. Assume that the coin flips follow the Bernoulli distribution $\\mathcal{Bern}(\\theta)$.\n",
"\n",
"- Derive the <font color='orange'>maximum likelihood estimate (MLE)</font> for parameter $p$\n",
"- Derive the <font color='orange'>maximum likelihood estimate (MLE)</font> for parameter $\\theta$\n",
"\n",
"$$\n",
"\\hat{\\theta}_\\text{MLE} = {\\arg \\max}_\\theta p(y | \\theta)\n",
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