FRM Part I · FRM Exam Part I · Random Variables
A continuous random variable X has probability density function f(x) = c·x for 0 ≤ x ≤ 2, and f(x) = 0 elsewhere. What is P(X > 1)?
P(X > 1) is 0.75. The density constant must be 0.5 so total probability is one, giving a CDF of x²/4. At x = 1 the CDF is 0.25, so the upper tail probability is 1 - 0.25 = 0.75.
- A0.25
- B0.50
- C0.75Correct
- D0.60
Explanation
Integrating c·x from 0 to 2 gives 2c = 1, so c = 0.5. The CDF is F(x) = x²/4 on [0,2]. P(X > 1) = 1 - F(1) = 1 - 0.25 = 0.75. The value 0.25 is P(X < 1), the wrong tail.
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