The following distribution is used in economics:
X = f ( x, a ) = a.x ^a-1 / 3^a for 0 ? x ? 3 and a >
1 and 0 otherwise
a) As a function of a what is the expected value for X ?
b) As a function of X what is th method of moments estimator for a ? ( x has bar on top)
c) If our sample gives X = 2 , then what is the moments estimate for a? ( x has bar on top)
d) As a function of a what is the expected value for X^2 ?
e) as a function of a what is the variance of X ?