2.6 () Make use of the result (2.265) to show that the mean, variance, and mode of the beta distribution (2.13) are given respectively by E[μ] = a a + b

(2.267)

var[μ] = ab

(a + b)2(a + b + 1)

(2.268)

mode[μ] = a − 1 a + b − 2. (2.269)