Topic: Probability and Stochastic Processes
Which distribution is memoryless?
- A. Normal
- B. Log-normal
- C. Exponential
- D. None of the above
Answer: C. Exponential
Explanation: The exponential distribution is the only continuous probability distribution that possesses the memoryless property. Mathematically, it satisfies $P(X > s + t | X > s) = P(X > t)$ for all $s, t > 0$. In the discrete domain, the geometric distribution is the only one with this property.