The probability distribution of a random variable X is
| \(X\) | 0 | 1 | 2 | 3 | 4 |
| \(P(X)\) | 0.2 | \(k\) | \(k\) | \(2k\) | \(k\) |
Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| (A) | value of \(k\) | (I) | \(\displaystyle\frac{16}{25}\) |
| (B) | \(P(x\ge 2)\) | (II) | \(\displaystyle\frac{9}{25}\) |
| (C) | \(P(x=3)\) | (III) | \(\displaystyle\frac{4}{25}\) |
| (D) | \(P(x \lt 2)\) | (IV) | \(\displaystyle\frac{8}{25}\) |
Choose the correct answer from the options given below.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(III), (B)-(I), (C)-(IV), (D)-(II)
The probabilities add up to 1:
\(0.2 + k + k + 2k + k = 1\)
\(5k = 0.8\)
(A) value of \(k\)
This matches (III) \(\frac{4}{25}\):
\( \displaystyle k = 0.16 = \frac{4}{25} \)
(B) \(P(x\ge 2)\)
This matches (I) \(\frac{16}{25}\):
\(P(2) + P(3) + P(4) = k + 2k + k = 4k\)
\( \displaystyle = 4 \times \frac{4}{25} = \frac{16}{25} \)
(C) \(P(x=3)\)
This matches (IV) \(\frac{8}{25}\):
\( \displaystyle P(3) = 2k = \frac{8}{25} \)
(D) \(P(x \lt 2)\)
This matches (II) \(\frac{9}{25}\):
\(P(0) + P(1) = 0.2 + 0.16 = 0.36\)
\( \displaystyle = \frac{9}{25} \)
So the matching is (A)-(III), (B)-(I), (C)-(IV), (D)-(II).