Question: Consider the beta distribution with parameters (a, b). Show that a. When a > 1 and b > 1, the density is unimodal (that is,

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 = b, all points in [0, 1] are modes.

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