Question

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 ...

• A. \(0.1\)
• B. \(0.2\)
• C. \(0.3\)
• D. \(0.5\)

Hint:

For a continuous variable, P(a < X < b) = F(b) - F(a).

Answer 1

The Correct Option is A

Step 1: Split the probability:
$P(X \leq b) = P(X \leq a) + P(a < X < b)$.

Step 2: Substitute:
$0.7 = 0.6 + P(a < X < b)$, so the required probability is $0.1$.

Final Answer:
The probability is $0.1$, option (A). \[ \boxed{0.1} \]