A continuous random variable X has a probability density f(x) = e-x, 0 < x < $$\infty $$ . Then P{X > 1} is A. 0.368 B. 0.5 C. 0.632 D. 1.0

$$f_X(x) = e^{-x}, \quad 0 < x < \infty$$

The probability that $X$ is greater than 1 is given by

$$P(X > 1) = \int_1^\infty f_X(x) dx = \int_1^\infty e^{-x} dx = \left[ -e^{-x} \right]_1^\infty = 1 – e^{-1} \approx 0.368$$

Option A is the correct answer. Option B is incorrect because the probability that $X$ is greater than 1 is not equal to 0.5. Option C is incorrect because the probability that $X$ is greater than 1 is not equal to 0.632. Option D is incorrect because the probability that $X$ is greater than 1 is not equal to 1.