19.X.2.3. Memoryless Nature

Try these first

1. 1.

   What does it mean for a process to be memoryless?

   Hint

   Think of an event that happens randomly.

2. 2.

   Give an example of a memoryless process.

   Hint

   Consider how past events affect your expectations for future events.

3. 3.

   What does memoryless nature imply in probability?

   • True
   • False

   Hint

   Consider events like waiting for something.

4. 4.

   In a Poisson process, does the occurrence of a previous event affect future probabilities?

   • Yes
   • No
   • Only in some cases

   Hint

   Think about independence.

5. 5.

   Imagine a server receives requests following a Poisson process with an average of 3 requests per minute. What is the probability that the server receives no requests in the next 5 minutes?

   Hint

   Remember to adjust λ for the time period.

6. 6.

   In a certain data transmission system, packets arrive in a Poisson manner with an average rate of 10 packets per second. What’s the probability of receiving exactly 7 packets in a 1-second interval?

   Hint

   Utilize the false assumption of dependence to visualize the independence.