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发帖数: 143 | 1 Let $X \sim N(0,1)$, $Y \sim \chi^2(n)$. Let $U=\frac{X}{\sqrt{\frac{Y}{n}}
}$, find the distribution of $U$.\vspace{1em}
$Y \sim \chi^2(n)$: \[f_{Y}(y)=\frac{1}{{\Gamma \left( {\frac{n}{2}} \right
)}}{y^{\frac{n}{2} - 1}}{\left( {\frac{1}{2}} \right)^{\frac{n}{2}}}{e^{ - \
frac{y}{2}}}\]
Let $V= Y$
\[
\begin{cases} X = U \sqrt{\frac{V}{n}}
\
Y = V
\end{cases}
\]
\[{\mathbf{J}} = \left| {\begin{array}{*{20}{c}}
{\frac{{\partial x}}{{\partial u}}} & {\frac{{\partial x}}{{\partial v}}}
\
|
|
