If the random variable x has the following distribution:

Match List-I with List-II

Choose the correct answer from the options given below.

(A)-(II), (B)-(III), (C)-(IV), (D)-(I)

The correct answer is Option (4) → (A)-(II), (B)-(III), (C)-(IV), (D)-(I) **

Given distribution:

X : 0, 1, 2
P(X) : k, k, 2k

Total probability = 1:

$k + k + 2k = 4k = 1 \Rightarrow k = \frac{1}{4}$

Now compute:

$P(x \ge 2) = P(2) = 2k = \frac{1}{2}$

$P(X \le 2) = P(0) + P(1) + P(2) = 1$

$P(0 < x \le 2) = P(1) + P(2) = k + 2k = 3k = \frac{3}{4}$

Final answer: (A)–(II), (B)–(III), (C)–(IV), (D)–(I)