When Y,,Y,.,Y, is a random sample from N(u,0), we learned in class that the has t distribution with n-1 degrees of freedom, where Y and S are statistic T = S/ n-1 the sample mean and sample standard deviation, respectively. Write out the form of T² and show algebraically that T2 can be written as the ratio of two independent x random variables, each divided by their respective degrees of freedom. What is, therefore, the distribution ofT?

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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When Y,,Y,..,Y, is a random sample from N(u,0), we learned in class that the
statistic T
S
" has t distribution with n-1 degrees of freedom, where Y and S are
the sample mean and sample standard deviation, respectively. Write out the form of T?
and show algebraically that T' can be written as the ratio of two independent x random
variables, each divided by their respective degrees of freedom. What is, therefore, the
distribution of T?
Transcribed Image Text:When Y,,Y,..,Y, is a random sample from N(u,0), we learned in class that the statistic T S " has t distribution with n-1 degrees of freedom, where Y and S are the sample mean and sample standard deviation, respectively. Write out the form of T? and show algebraically that T' can be written as the ratio of two independent x random variables, each divided by their respective degrees of freedom. What is, therefore, the distribution of T?
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