A continuous random variable X has a probability density function f(x) = e^-x, 0 1) is: - Mathematics MCQ Mathematics Mock Test - 3 2026 | ExamTest.live

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1 mark

A continuous random variable X has a probability density function f (x) = e^{- x}, 0 < x < \infty . Then P (X > 1) is:

Solution & Step-by-step Explanation

P (X > 1) = \int_{1}^{\infty} f (x) d x = \int_{1}^{\infty} e^{- x} d x P (X > 1) = [- e^{- x}]_{1}^{\infty} = - e^{- \infty} - (- e^{- 1}) P (X > 1) = 0 + e^{- 1} = \frac{1}{e}

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A continuous random variable X has a probability density function f (x) = e^{- x}, 0 < x < \infty . Then P (X > 1) is:

1/ e

e

1

Data insufficient

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