The Gamma distribution Gamma ( a , $ ) with paramters a gt; O , and $ gt; O is defined by the density* fap ( x ) = 18^ - Too * * - e-#*, for allx 2...

a) What is the asymptotic variance of alpha_hat?

b) Using the previous part, find the confidence intervals for alpha with asymptotic level 90% using both the "solving" and "plug-in"methods. Use n=25 and Xn_bar= 4.5

The Gamma distribution Gamma ( a , $ ) with paramters a > O , and $ > O is defined by the density*fap ( x ) = 18^- Too * * - e-#*, for allx 2 0.The I function is defined by[ ( S ) =\ x `- le - * dix .As Usual , the constant $It Is a normalization constant that gives / faq ( * ) dx = 1 .In this problem , let * 1 . .... In bei.i.d . Gamma variables withB = - for some a > O .That is ,* * 1 . .... In ~ Gamma ( a , & ) random variables for some a > O . The pof for* ; is therefore*1Jalx ) _ _ _^e-^, for all x 2 0.