GATE 2026 DA – Question 34
Let $X$ be an exponentially distributed random variable with mean $\lambda\ (> 0)$. If $P(X > 5) = 0.35$, then the conditional probability $P(X > 10 \mid X > 5)$ is ___________ . (*Rounded off to two decimal places*)
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Correct answer: 0.34 to 0.36
Explanation
The exponential distribution has no memory: $P(X > 10 \mid X > 5) = P(X > 5)$. Directly, $P(X > 10 \mid X > 5) = \frac{P(X > 10)}{P(X > 5)} = \frac{e^{-10/\lambda}}{e^{-5/\lambda}} = e^{-5/\lambda} = 0.35$.