Show that x1x2 is a pivotal quantity and construct a

Question

Let X_i, i = 1, 2, be independent with the p.d.f.'s λ_ie^-λixI_(0,∞)(x), i = 1, 2, respectively.

(a) Let θ = λ₁/λ₂. Show that θX₁/X₂ is a pivotal quantity and construct a confidence interval for θ with confidence coefficient 1 - α, using this pivotal quantity.

(b) Let θ = (λ₁, λ₂). Show that λ₁X₁ + λ₂X₂ is a pivotal quantity and construct a confidence set for θ with confidence coefficient 1 - α, using this pivotal quantity.