The probability distribution of a random variable X is

Match List-I with List-II

Choose the correct answer from the options given below.

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

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

Given probability distribution:

Total probability = 1

$0.2 + k + k + 2k + k = 1$

$0.2 + 5k = 1 \Rightarrow 5k = 0.8 \Rightarrow k = 0.16$

(A) value of k = 0.16 = $\frac{4}{25}$ → (III)

(B) $P(x \ge 2) = P(2)+P(3)+P(4)=k+2k+k=4k=4(0.16)=0.64=\frac{16}{25}$ → (I)

(C) $P(x=3)=2k=0.32=\frac{8}{25}$ → (IV)

(D) $P(x<2)=P(0)+P(1)=0.2+k=0.36=\frac{9}{25}$ → (II)

Matching:

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