Let the pdf f(x; 1 , 2 ) be of the form exp[p 1 (

Let the pdf f(x; θ₁, θ₂) be of the form

exp[p₁(θ₁, θ₂)K₁(x) + p₂(θ₁, θ₂)K₂(x) + H(x) + q₁(θ₁, θ₂)], a < x < b,
zero elsewhere. Suppose that K'₁(x) = cK'₂(x). Show that f(x; θ₁, θ₂) can be written in the form
exp[p(θ₁, θ₂)K₂(x) + H(x) + q(θ₁, θ₂)], a < x < b,
zero elsewhere. This is the reason why it is required that no one K'_j(x) be a linear homogeneous function of the others, that is, so that the number of sufficient statistics equals the number of parameters.