exercise:8aa565e4c5: 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> Previous experience with a drug suggests that the probability <math>p</math> that the drug is effective is a random quantity having a beta density with parameters <math>\alpha = 2</math> and <math>\beta = 3</math>. The drug is used on ten subject...") |
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Previous experience with a drug suggests that the probability <math>p</math> that the drug is effective is a random quantity having a beta density with | |||
the drug is effective is a random quantity having a beta density with | |||
parameters <math>\alpha = 2</math> and <math>\beta = 3</math>. The drug is used on ten subjects and | parameters <math>\alpha = 2</math> and <math>\beta = 3</math>. The drug is used on ten subjects and | ||
found to be successful in four out of the ten patients. What density should we | found to be successful in four out of the ten patients. What density should we now assign to the probability <math>p</math>? What is the probability that the drug will be successful the next time it is used? | ||
now assign to the probability <math>p</math>? What is the probability that the drug will | |||
be successful the next time it is used? | |||
Latest revision as of 00:43, 14 June 2024
Previous experience with a drug suggests that the probability [math]p[/math] that the drug is effective is a random quantity having a beta density with parameters [math]\alpha = 2[/math] and [math]\beta = 3[/math]. The drug is used on ten subjects and found to be successful in four out of the ten patients. What density should we now assign to the probability [math]p[/math]? What is the probability that the drug will be successful the next time it is used?