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📐 Mathematics  ·  Probability  ·  JEE

Exponential distribution is the only continuous distribution with the memoryless property. P(X > s + t | X > s) =

Answer: P(X > t) - independent of past waiting time.

  • A P(X > s), reusing the original condition as the answer
  • B P(X > t) - independent of past waiting time
  • C P(X > s+t), the unconditional probability of exceeding s+t
  • D e<sup>-lambda</sup>, a constant with no dependence on s or t at all

Correct answer: B. P(X > t) - independent of past waiting time

Explanation: Memoryless: P(X > s+t | X > s) = P(X > t). Past waiting time is irrelevant. Only exponential has this property among continuous distributions.

UABA and BA onlyB onlyOutside both circles: complement of (A union B)

Venn diagram of the universal set U with events A and B, showing the intersection (A and B), the parts unique to each event, and the complement region outside both.

Concept context

Chance, events, conditional probability, and Bayes theorem

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