1 This exercise investigates properties of the Beta distribution defined in Equation (6). a. By integrating over...

1 This exercise investigates properties of the Beta distribution defined in Equation (6).

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a. By integrating over the range [0, 1], show that the normalization constant for the dis- tribution beta[a, b] is given by a = (a + b)/T(a) (b) where F(x) is the Gamma function, defined by (x+1)=x F(x) and F(1) = 1. (For integer x, F(x+1)=x!.) b. Show that the mean is a/(a + b). c. Find the mode(s) (the most likely value(s) of 0). d. Describe the distribution beta[e, e] for very small e. What happens as such a distribution is updated?