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 $\left({\mathit{X}}^2\right)$ = Σ ${\mathit{x}}^2$ P (X) = 17
⇒ V (X) = E $\left({\mathit{X}}^2\right)$ - ${\left[\mathit{E}\left(\mathit{X}\right)\right]}^2$
⇒ V (X) = 17 - ${\left[4\right]}^2$
⇒ V (X) = 1