Let X1 and X2 be a random sample of size n 2 from a continu

Let X₁ and X₂ be a random sample of size n = 2 from a continuous distribution with pdf of the form f(x) = 2x if 0 < x < 1 and zero otherwise.

(a) Find the marginal pdfs of the smallest and largest order statistics, Y₁ and Y₂.

(b) Find the joint pdf of Y₁ and Y₂.

(c) Find the pdf of the sample range R = Y₂ – Y₁.

Solution