A random variable X has the following probability distribution:
| X | 0 | 1 | 2 | 3 | 4 |
| P(X) | 0.1 | 0.15 | 0.30 | 0.30 | 0.15 |
Which of the following are correct?
(A) P(X \( \le \) 1) = 0.25
(B) P(X \( \gt \) 3) = 0.15
(C) P(X = 2) = 0.30
(D) P(X \( \le \) 2) = 0.55
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A), (B), (C) and (D)
Each probability is the sum of the table values for the required values of X:
\( \displaystyle P(X\le 1)=P(X=0)+P(X=1)=0.1+0.15=0.25 \)
\( \displaystyle P(X\gt 3)=P(X=4)=0.15 \)
\( \displaystyle P(X=2)=0.30 \)
\( \displaystyle P(X\le 2)=0.1+0.15+0.30=0.55 \)
So P(X ≤ 1) = 0.25, P(X > 3) = 0.15, P(X = 2) = 0.30 and P(X ≤ 2) = 0.55.
Checking the statements
(A) P(X \( \le \) 1) = 0.25 — Correct. 0.1 + 0.15 = 0.25.
(B) P(X \( \gt \) 3) = 0.15 — Correct. Only X = 4 is greater than 3, and P(X = 4) = 0.15.
(C) P(X = 2) = 0.30 — Correct. Read directly from the table.
(D) P(X \( \le \) 2) = 0.55 — Correct. 0.1 + 0.15 + 0.30 = 0.55.