GATE 2024 IN – Question 65
A random variable $X$ has density $f_X(x)=e^{-x}$ for $x\ge0$ and zero otherwise. The probability $P(X>2)$ is ______ (three decimal places).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.130 to 0.140
Explanation
Integrate the density over the requested tail: $P(X>2)=\int_2^\infty e^{-x}\,dx=e^{-2}=0.135335\ldots$. To three decimals the answer is **0.135**.