## – Stochastic Process course notes

## 1. Definition

- Probability function: ,
- Cumulative Distribution Function (CDF): ,
- Complement of the CDF (CCDF): , .

**2. Memoryless Property**

**A random variable X has the memoryless property if**

__Def`1__:** Def`2: **A random variable X has the memoryless property if

The exponential distribution is the only distribution that has the memoryless property (Satisfy definition 2)

**3. Useful Properties: First occurrence among events**

Assume are exponential variable with rate .

Then what is the probability that .

More generally

## 4. Distribution of time of first event

This is the CDF of an exponential RV with rate , therefore

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