Mathematical statistics - Uniformly minimum variance unbiased estimator (UMVUE)

I wish I would get all parts of answers, but I want to get answers ofpart (d) and (e), specifically.

Thank you.

Suppose that X is a single observation from a NV(0, 0) distribution where d > 0 is unknown. Use the following steps to construct the uniformly minimum variance unbiased estimator (UMVUE) for A based on X. (a) Show that T = [X | is complete and sufficient for 0. (b) Show that the density of T is g (t ) = (270) 1/2 expl-7(t - 0)?}{1 + exp(-2t) }, if t > 0; 0 , otherwise. (c) Show that for t > 0, Pr(X = tT = t) = exp(t)/{exp(-t) + exp(t) }.\f