A random variable X has the following probability distribution:

then which of the following are TRUE?

(A) $k=0.1$

(B) $P(X < 1) = 0.4$

(C) $P(X < 2) = 0.7$

(D) $P(0 < x < 3) = 0.5$

Choose the correct answer from the options given below.

(A), (B), (C) and (D)

The correct answer is Option (3) → (A), (B), (C) and (D) **

Given probabilities:

$0.1,\;0.2,\;k,\;0.3,\;2k,\;0.1$

Sum must be 1:

$0.1+0.2+k+0.3+2k+0.1 = 1$

$0.7 + 3k = 1$

$3k = 0.3$

$k = 0.1$ ✔

Now check statements:

(A) $k = 0.1$ ✔

(B) $P(X < 1) = P(-2)+P(-1)+P(0)$

$= 0.1 + 0.2 + 0.1 = 0.4$ ✔

(C) $P(X < 2) = P(-2) + P(-1) + P(0) + P(1)$

$= 0.1 + 0.2 + 0.1 + 0.3 = 0.7$ ✔

(D) $P(0 < X < 3) = P(1) + P(2)$

$= 0.3 + 0.2 = 0.5$ ✔

Correct statements: (A), (B), (C), (D)