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**Theorem:** Let $X$ be an $n \times 1$ [random vector](/D/rvec) with possible outcomes $\mathcal{X}$ and let $g: \; \mathbb{R}^n \rightarrow \mathbb{R}^n$ be an invertible function on the support of $X$. Then, the [probability mass function](/D/pmf) of $Y = g(X)$ is given by
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**Theorem:** Let $X$ be an $n \times 1$ [random vector](/D/rvec)of [discrete random variables](/D/rvar-disc)with possible outcomes $\mathcal{X}$ and let $g: \; \mathbb{R}^n \rightarrow \mathbb{R}^n$ be an invertible function on the support of $X$. Then, the [probability mass function](/D/pmf) of $Y = g(X)$ is given by
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