Question:

Suppose a random variable 𝑋 follows an exponential distribution with mean 50. Then, the value of the conditional probability $ P(X > 70 | X > 60)$ is

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Updated On: Feb 10, 2025
  • $e^{\frac{βˆ’ 7}{ 5}}$
  • $e^{\frac{βˆ’6}{ 5}}$
  • $e^{\frac{βˆ’ 1}{ 5}}$
  • $e^{\frac{βˆ’ 7}{ 6}}$
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The Correct Option is C

Solution and Explanation

Memoryless Property of Exponential Distribution

For an exponential distribution, the memoryless property applies, meaning: 

P(X > s + t | X > s) = P(X > t)

Here, we have:

  • t = 70 βˆ’ 60 = 10
  • The rate parameter Ξ» = 1/50

Using the exponential survival function:

P(X > 10) = eβˆ’Ξ» Γ— 10

Substituting the value of Ξ»:

P(X > 10) = eβˆ’1/5

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