solutions2_chapter3

# solutions2_chapter3 - The solution is correct if both α...

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3.27 Comment: A density f ( x ) will be unimodal if its derivative f 0 ( x ) has one sign change, going from + to - . It will also be unimodal (with mode at the left endpoint of the support) if the derivative is always negative. It will be unimodal (with mode at the right endpoint of the support) if the derivative is always positive. 3.27(b) The solution in the manual is only correct for α > 1. For 0 < α 1, the density is unimodal with mode at zero. 3.27(d)
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Unformatted text preview: The solution is correct if both α > 1 and β > 1. If both α < 1 and β < 1, then the density is not unimodal; the density has two peaks (at x = 0 and x = 1). If α < 1 and β ≥ 1, then it is unimodal with mode at x = 0. If α ≥ 1 and β < 1, then it is unimodal with mode at x = 1. If α = β = 1, then the density is uniform; it is unimodal and any value x ∈ [0 , 1] can be taken as the mode. 1...
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## This note was uploaded on 12/15/2011 for the course STAT 5326 taught by Professor Frade during the Fall '10 term at FSU.

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solutions2_chapter3 - The solution is correct if both α...

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