Question

If the probability density function of a random variable \( X \) is \( f(x) = \frac{x}{2} \) for \( 0 \leq x \leq 2 \), then \[ P(X>1.5 \mid X>1) \] is equal to

• A. \( \frac{7}{16} \)
• B. \( \frac{3}{4} \)
• C. \( \frac{21}{64} \)
• D. \( \frac{1}{5} \)

Hint:

For conditional probability, use the formula \( P(A \mid B) = \frac{P(A \cap B)}{P(B)} \).

Answer 1

The Correct Option is C

Step 1: Conditional probability formula.
We use the formula \( P(A \mid B) = \frac{P(A \cap B)}{P(B)} \) to find the conditional probability. Calculate \( P(X>1.5) \) and \( P(X>1) \) using the given probability density function.

Step 2: Conclusion.
Thus, the correct answer is option (C).

Final Answer: \[ \boxed{\text{(C) } \frac{21}{64}} \]