Question

To the best of your ability, explain in words why the memoryless property does not apply to the following random variable types specifically:

• Binomial random variables

• Poisson random variables

• Pascal random variables

Answer 1

Memoryless property is applicable when the information is the previous trials has no impact.

In Binomial distribution we are counting the number of success, there is an impact of the results obtain in the previous trials. It might increase the number of success.

Similar for poisson distribution, lets assume that a random variable count the number of misprint. So there is an impact of the outcome in the previous trials.

Similarly in pascal the random variable denotes the number of failures that precede the rth success.

On the contrary in geometric distribution we consider the first success. And as soon as the first success occurs we stop the experiment. We are not using that information in the next steps.