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1
Marks: +2.0, -0.66
Let \( X \) and \( Y \) be two independent random variables with probability density functions \( f_X(x) = e^{-x} \) for \( x > 0 \) and \( f_Y(y) = 2e^{-2y} \) for \( y > 0 \). What is the probability that \( X > Y \)?
A) \( \frac{1}{3} \)
B) \( \frac{2}{3} \)
C) \( \frac{1}{2} \)
D) \( \frac{1}{4} \)
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