Find mode of a chi-square variate with 8 degrees of freedom.
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We need to find x∗ such that x∗=argmaxx>0f(x). Then x∗ is the mode. Note that argmaxx>0f(x)=argmaxx>0logf(x), so we will find the mode by maximizing the log of the pdf instead of maximizing the pdf (this turns out to be easier).
Explanation:
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