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{
    "url": "https://numbas.mathcentre.ac.uk/api/questions/11890/?format=api",
    "name": "Log-likelihood and maximum likelihood estimator for PDF",
    "published": true,
    "project": "https://numbas.mathcentre.ac.uk/api/projects/601/?format=api",
    "author": {
        "url": "https://numbas.mathcentre.ac.uk/api/users/697/?format=api",
        "profile": "https://numbas.mathcentre.ac.uk/accounts/profile/697/?format=api",
        "full_name": "Newcastle University Mathematics and Statistics",
        "pk": 697,
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    "edit": "https://numbas.mathcentre.ac.uk/question/11890/log-likelihood-and-maximum-likelihood-estimator-fo/?format=api",
    "preview": "https://numbas.mathcentre.ac.uk/question/11890/log-likelihood-and-maximum-likelihood-estimator-fo/preview/?format=api",
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    "source": "https://numbas.mathcentre.ac.uk/question/11890/log-likelihood-and-maximum-likelihood-estimator-fo.exam?format=api",
    "metadata": {
        "notes": "<p><strong>14/07/2012:</strong></p>\n        <p>Added tags.</p>\n        <p>Corrected mistakes in Advice.</p>\n        <p>Added some text to make statement clearer re parameter $t$.</p>\n        <p>Rephrased questions in last question so that it is clear that the value to 2dps is used in the calculation.</p>\n        <p>Spaced Advice text.</p>\n        <p>New tolerance variable, &nbsp;tol=0 for last two questions.</p>\n        <p>Added line in prompt: If $\\ln(a)$, for some integer $a$, is a term in your answer, leave as $\\ln(a)$ and do not evaluate.</p>\n        <p>Improved display of correct answer in second question as $+\\;- $ together. Also improved correct answer display in second last question.</p>\n        <p>Important: set checking range between -0.2 and -0.1 rather than between 0 and 1 so that evaluation of likelihood function over the range does not suffer from underflow and incorrect answer marked as correct. This needs constant testing, have tested on bounday values and OK.</p>\n        <p><strong>1/08/2012:</strong></p>\n        <p>Added tags.</p>\n        <p>In the Advice section, moved \\Rightarrow to the beginning of the line instead of the end of the previous line.</p>\n        <p><strong>21/12/2012:</strong></p>\n        <p>Checked calculations, OK. Added tested1 tag.</p>\n        <p>Checked rounding, OK. Added cr1 tag.</p>\n        <p>Scenarios, so added sc tag.</p>",
        "licence": "Creative Commons Attribution 4.0 International",
        "description": "<p>Given a PDF $f(x)$ on the real line with unknown parameter $t$ and three random observations, find log-likelihood and MLE $\\hat{t}$ for $t$.&nbsp;</p>"
    },
    "status": "ok",
    "resources": []
}