## What does memoryless property mean?

In probability and statistics, memorylessness is a property of certain probability distributions. It usually refers to the cases when the distribution of a “waiting time” until a certain event does not depend on how much time has elapsed already.

**What is the memoryless property of a distribution?**

The memoryless property (also called the forgetfulness property) means that a given probability distribution is independent of its history. Any time may be marked down as time zero.

### What does it mean to say that the exponential distribution is memoryless?

If X is exponential with parameter λ>0, then X is a memoryless random variable, that is P(X>x+a|X>a)=P(X>x), for a,x≥0. From the point of view of waiting time until arrival of a customer, the memoryless property means that it does not matter how long you have waited so far.

**Is Markov process memoryless?**

In probability theory and statistics, the memoryless property of a stochastic process is called Markov property. In fact, a stochastic process has the Markov property if only the present state of a process affects on the conditional probability distribution of a future state.

## Does Poisson have memoryless property?

On the other hand, a Poisson process is a memoryless stochastic point process; that an event has just occurred or that an event hasn’t occurred in a long time give us no clue about the likelihood that another event will occur soon.

**What is non markovian?**

Non-Markovian dynamics constitute any interaction between a system and its environment which then affects the system at a later time; the environment need not even be coherent.

### Is Poisson distribution memoryless?

**Which of the following discrete random variable follows memoryless property?**

The only memoryless discrete probability distributions are the geometric distributions.

## What is a memoryless random variable?

A random variable X is memoryless if for all numbers a and b in its range, we have. P(X>a + b|X>b) = P(X>a) . (1) (We are implicitly assuming that whenever a and b are both in the range of X, then so is a+b. The memoryless property doesn’t make much sense without that assumption.)