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) =

2

20

For X 3, possibilities are (1 , 3) , (2 , 3) , (3 , 1) , (3 , 2)
∴ P (X = 3) =

4

20

For X = 4, possibilities are (1 , 4) , (2 , 4) , (3 , 4) , (4 , 3) , (4 , 2) , (4 , 1)
∴ P (X = 4) =

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) =

8

20

⇒ E (X) = Σ x P (x) = 4 and E (X2) = Σ x2 P (X) = 17
⇒ V (X) = E (X2) - [E(X)]2
⇒ V (X) = 17 - [4]2
⇒ V (X) = 1