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

• A. $e^{\frac{− 7}{ 5}}$
• B. $e^{\frac{−6}{ 5}}$
• C. $e^{\frac{− 1}{ 5}}$
• D. $e^{\frac{− 7}{ 6}}$

Hint:

148

Answer 1

The Correct Option is C

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 − 60 = 10
• The rate parameter λ = 1/50

Using the exponential survival function:

P(X > 10) = e^{−λ × 10}

Substituting the value of λ:

P(X > 10) = e^−1/5