Question: 2. Let X1, . . . , X be an i.i.d. sample from a distribution with the frequency function gimpw, m=l,2,..., Where 9 > 0

2. Let X1, . . . , X\" be an i.i.d. sample from a distribution with the frequency function gimpw, m=l,2,..., Where 9 > 0 and log denotes the natural logarithm. The mean of this distribution is (1 + 6) log(1 + 1/9). (i) Does the given distribution belong to the exponential family of distributions? Justify your answer. (ii) Find a sufcient statistic for 6. (iii) Show that the mle of 6 is a solution of the equation 9(6) = X, Where X is the sample mean. You need to give an explicit expression for 9(0). (iv) Find the asymptotic variance of the mle

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