exercise:D9855c5ec9: Difference between revisions
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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> A drug is assumed to be effective with an unknown probability <math>p</math>. To estimate <math>p</math> the drug is given to <math>n</math> patients. It is found to be effective for <math>m</math> patients. The ''method of maximum likelihood''...") |
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A drug is assumed to be effective with an unknown probability <math>p</math>. To estimate <math>p</math> the drug is given to <math>n</math> patients. It is found to be effective for <math>m</math> patients. The ''method of maximum likelihood'' | |||
<math>p</math>. To estimate <math>p</math> the drug is given to <math>n</math> patients. It is found to be effective | |||
for <math>m</math> patients. The ''method of maximum likelihood'' | |||
for estimating <math>p</math> states that we should choose the value for <math>p</math> that gives the | for estimating <math>p</math> states that we should choose the value for <math>p</math> that gives the | ||
highest probability of getting what we got on the experiment. Assuming that the experiment | highest probability of getting what we got on the experiment. Assuming that the experiment | ||
can be considered as a Bernoulli trials process with probability <math>p</math> for success, show | can be considered as a Bernoulli trials process with probability <math>p</math> for success, show | ||
that the maximum likelihood estimate for <math>p</math> is the proportion <math>m/n</math> of successes. | that the maximum likelihood estimate for <math>p</math> is the proportion <math>m/n</math> of successes. | ||
Latest revision as of 00:07, 13 June 2024
A drug is assumed to be effective with an unknown probability [math]p[/math]. To estimate [math]p[/math] the drug is given to [math]n[/math] patients. It is found to be effective for [math]m[/math] patients. The method of maximum likelihood for estimating [math]p[/math] states that we should choose the value for [math]p[/math] that gives the highest probability of getting what we got on the experiment. Assuming that the experiment can be considered as a Bernoulli trials process with probability [math]p[/math] for success, show that the maximum likelihood estimate for [math]p[/math] is the proportion [math]m/n[/math] of successes.