Exponential Distribution: Memoryless Property
1. Context
In this video from the FRM Part 1 curriculum, we take a look at the “memoryless” property of exponential distribution.
| Area | Quantitative Analysis |
| Reading | Common Univariate Random Variables |
| Reference | Chapter 3, Common Univariate Random Variables, GARP Official Books (Book 2, Quantitative Analysis). |
2. Video
3. Transcript
Exponential variables are memoryless. To understand this concept, consider the example of a company’s random default time (denoted by $T_{def}$, which is exponentially distributed with a constant parameter, $\beta$. If we want to calculate the conditional probability of this company defaulting over a future period of time (of length or duration $t$), given it has already survived for a certain period, the memoryless property of $T_{def}$ implies that it has no memory of the elapsed time.
Therefore, the desired conditional probability can be calculated as an unconditional probability for the upcoming period of duration $t$, starting from today. This probability can be determined using the CDF of the random default time, given by: $$ F_{T_{def}} = 1 – \exp \left(-\frac{t}{\beta} \right) $$
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