exercise:92bf4011a3: 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> Assume that a student going to a certain four-year medical school in northern New England has, each year, a probability <math>q</math> of flunking out, a probability <math>r</math> of having to repeat the year, and a probability <math>p</math> of...") |
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\newcommand{\mathds}{\mathbb}</math></div> Assume that a student going to a certain four-year | \newcommand{\mathds}{\mathbb}</math></div> Assume that a student going to a certain four-year medical school in northern New England has, each year, a probability <math>q</math> of flunking out, a probability <math>r</math> of having to repeat the year, and a probability <math>p</math> of moving on to the next year (in the fourth year, moving on means graduating). | ||
medical | <ul style="list-style-type:lower-alpha"><li> Form a transition matrix for this process taking as states F, 1, 2, 3, | ||
school in northern New England has, each year, a probability <math>q</math> of flunking | |||
out, a | |||
probability <math>r</math> of having to repeat the year, and a probability <math>p</math> of moving | |||
on to the next year (in the fourth year, moving on means graduating). | |||
<ul><li> Form a transition matrix for this process taking as states F, 1, 2, 3, | |||
4, and G where F stands for flunking out and G for graduating, and the other | 4, and G where F stands for flunking out and G for graduating, and the other | ||
states represent the year of study. | states represent the year of study. | ||
Latest revision as of 22:43, 15 June 2024
[math]
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\newcommand{\secstoprocess}{\all}
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\newcommand{\mathds}{\mathbb}[/math]
Assume that a student going to a certain four-year medical school in northern New England has, each year, a probability [math]q[/math] of flunking out, a probability [math]r[/math] of having to repeat the year, and a probability [math]p[/math] of moving on to the next year (in the fourth year, moving on means graduating).
- Form a transition matrix for this process taking as states F, 1, 2, 3, 4, and G where F stands for flunking out and G for graduating, and the other states represent the year of study.
- For the case [math]q = .1[/math], [math]r = .2[/math], and [math]p = .7[/math] find the time a beginning student can expect to be in the second year. How long should this student expect to be in medical school?
- Find the probability that this beginning student will graduate.