Given that two positive integers can be selected from the first 5 positive integers without replacement in 5 × 4 = 20 ways. X represents the larger of the two numbers obtained. Hence, X can be 2, 3, 4, 5. For x = 2, possibilities are (1, 2) and (2, 1). ∴ P (X = 2) = $\frac{2}{20}$ For X 3, possibilities are (1 , 3) , (2 , 3) , (3 , 1) , (3 , 2) ∴ P (X = 3) = $\frac{4}{20}$ For X = 4, possibilities are (1 , 4) , (2 , 4) , (3 , 4) , (4 , 3) , (4 , 2) , (4 , 1) ∴ P (X = 4) = $\frac{6}{20}$ For X = 5, possibilities are (1 , 5) , (2 , 5) , (3 , 5) , (4 , 5) , (5 , 4) , (5 , 3) , (5 , 2) , (5 , 1) ∴ P (X = 5) = $\frac{8}{20}$ ⇒ E (X) = Σ x P (x) = 4 and E $(X^2)$ = Σ $x^2$ P (X) = 17 ⇒ V (X) = E $(X^2)$ - $[E(X)]^2$ ⇒ V (X) = 17 - $[4]^2$ ⇒ V (X) = 1