Question: 4. Let X, X,***, X, be IID Gamma(a, b) random variables with common density function f(x; , B) = 1 -xa-1 e , x>

4. Let X, X,***, X, be IID Gamma(a, b) random variables with

4. Let X, X,***, X, be IID Gamma(a, b) random variables with common density function f(x; , B) = 1 -xa-1 e , x> 0, where a > 0, > 0 are unknown. Derive a two-dimensional minimal sufficient statistic for Bar(a) (a,). 5. Let X, XX, be IID having a Beta (, ) distribution with common density function -15 f(x,a,p)= T(a+B) (a)() x-(1-x)-1,0 0, >0 are the unknown parameters. Derive the minimal sufficient statistic for (a,).

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