Let x1 and x2 be independent random samples with densities f

Let x₁ and x₂  be independent random samples with densities f₁(x₁) = xe^(-theta*x₁) and

f₂(x₂) = 2thetae^(-2theta*x₂) respectively, where theta greater than 0 is an unknown parameter, and

0 is less than x₁, x₂ is less than infinity .

Find a sufficient statistic for theta.

Solution