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corrected some pages
Several small corrections were done to several proofs and definitions.
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P/mult-test.md

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such that the probability of observing the counts $y$, given $H_0$, is
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$$ \label{eq:Pr0-y}
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\mathrm{Pr}(y \vert H_0) = n! \prod_{j=1}^k \frac{{p_{0i}}^{y_j}}{y_j!} \; .
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\mathrm{Pr}(y \vert H_0) = n! \prod_{j=1}^k \frac{ {p_{0i}}^{y_j} }{y_j!} \; .
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$$
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The probability of observing any other set of counts $x$, given $H_0$, is
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$$ \label{eq:Pr0-x}
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\mathrm{Pr}(x \vert H_0) = n! \prod_{j=1}^k \frac{{p_{0i}}^{x_j}}{x_j!} \; .
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\mathrm{Pr}(x \vert H_0) = n! \prod_{j=1}^k \frac{ {p_{0i}}^{x_j} }{x_j!} \; .
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$$
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The [p-value](/D/pval) is the probability of observing a value of the [test statistic](/D/tstat) that is as extreme or more extreme then the actually observed test statistic. Any set of counts $x$ might be considered as extreme or more extreme than the actually observed counts $y$, if the former is equally probable or less probably than the latter:

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