Let r v s X 1 and X 2 be both distributed with a common scale parameter a and essential parameters 1 and 2 1 2 Show that X 1 dominates X 2 in the sense of the FSD Can we claim that P(X 1 X 2 ) 1 (Advice To answer the second question, we may assume X 1 and X 2 to be independent ) ...

Let X3 be independent of X2 and have the Fdistri ...

Let r.v.s X 1 and X 2 be both -distributed with a common scale parameter a and

Question:

Let r.v.’s X₁ and X₂ be both Γ-distributed with a common scale parameter a and “essential” parameters ν₁ and ν₂; ν₁ > ν₂. Show that X₁ dominates X₂ in the sense of the FSD. Can we claim that P(X₁ ≥ X₂) = 1? (Advice: To answer the second question, we may assume X₁ and X₂ to be independent.)