Q99 / 150 · MHT CET 2026 (18 April Shift 1) · Mathematics
Let $F(x)$ be the cumulative distribution function (c.d.f.) of a continuous random variable $X$. If $F(b) = 0.7$ and $P(X > a) = 0.4$, then the value of $P(a < X < b)$ is ...
- Correct answerA$0.1$
- B$0.2$
- C$0.3$
- D$0.5$
Solution
The cumulative distribution function $F(x)$ is defined as $F(x) = P(X \le x)$.
Given $F(b) = 0.7$, we have $P(X \le b) = 0.7$.
We are also given $P(X > a) = 0.4$.
Since $P(X \le a) + P(X > a) = 1$, we get:
$P(X \le a) = 1 - 0.4 = 0.6$
For a continuous random variable, the probability $P(a < X < b)$ is given by:
$P(a < X < b) = P(X \le b) - P(X \le a)$
Substituting the values:
$P(a < X < b) = 0.7 - 0.6 = 0.1$
Answer: $0.1$
Given $F(b) = 0.7$, we have $P(X \le b) = 0.7$.
We are also given $P(X > a) = 0.4$.
Since $P(X \le a) + P(X > a) = 1$, we get:
$P(X \le a) = 1 - 0.4 = 0.6$
For a continuous random variable, the probability $P(a < X < b)$ is given by:
$P(a < X < b) = P(X \le b) - P(X \le a)$
Substituting the values:
$P(a < X < b) = 0.7 - 0.6 = 0.1$
Answer: $0.1$
Hence, the correct answer is option: 'A'.