Skip to content
GATEiit

GATE DA 2026 Q34: Memoryless property of the exponential distribution

Question

Let XX be an exponentially distributed random variable with mean λ (>0)\lambda\ (> 0). If P(X>5)=0.35P(X > 5) = 0.35, then the conditional probability P(X>10∣X>5)P(X > 10 \mid X > 5) is ___________. (Rounded off to two decimal places)

Try it: numerical answer: type the value

Numerical answer. No negative marking.
Show answer and explanation

Answer: 0.34 to 0.36 (official GATE 2026 final answer key)

Concept used: Memoryless property: P(X>s+t∣X>s)=P(X>t)P(X > s + t \mid X > s) = P(X > t).

First step: P(X>10∣X>5)=P(X>5)P(X > 10 \mid X > 5) = P(X > 5).

Full step-by-step solution

Detailed working, common mistakes and linked mock tests will be available with a free GATEiit account. Log-in is coming soon.

Share this question

WhatsAppDownload image

Source: official GATE 2026 DA question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

More Probability and Statistics PYQs

PracticePractise Probability and Statistics questions →Full paperAll GATE DA 2026 questions →