Question

In: Statistics and Probability

In a Poisson process, the probability of a single occurrence of the event in a given...

In a Poisson process, the probability of a single occurrence of the event in a given interval is
proportional to the dimension of the interval.

Solutions

Expert Solution

The probability of a single occurrence of an event in a given interval is given by

where is the average number of occurrence in the given interval.

If the dimension of the interval increases, then the average number of occurrences in that interval will also increase, so will increase.

The function is .

The derivative of the above function is

Now, is always positive, and is positive only when is less than 1, but if the dimension of the interval will increase, then will also increase and in that case the derivative will be negative, if becomes greater than 1.

So, we have the following conclusion,

increases for and decreases for .

So, the probability of a single occurrence of an event in a given interval is proportional for and inversely proportional if the dimension of the interval increases furthur.

Thank You!! Please Upvote!!

orchestra answered 2 years ago
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