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In frequentist hypothesis testing, the $p$-value is the probability of a result as extreme (or more) than the observed result, under the assumption that the null hypothesis is true.
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What is the integral of the t-distribution function?
The t-distribution probability density function is given by:
$f(x) = \frac{\Gamma(\frac{\nu+1}{2})}{\sqrt{\nu\pi}\Gamma(\frac{\nu}{2})}(1+\frac{x^2}{\nu})^{-\frac{\nu+1}{2}}$
Is there an integral o …