Consider the beta distribution with parameters (a, b). Show that
(a) when a > 1 and b > 1, the density is unimodal (that is, it has a unique mode) with mode equal to (a − 1 )/(a + b − 2);
(b) when a ≤ 1, b ≤ 1, and a + b < 2, the density is either unimodal with mode at 0 or 1 or U-shaped with modes at both 0 and 1;
(c) when a = 1 = 6, all points in [0,1 ] are modes.
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