Question

The city of Seattle reports that there is an average of 1.67 fatal vehicle collisions per month in the city limits. You are interested in the probability of seeing a particular number of fatal collisions during a given month in Seattle.

Let Y be the number of months at which the first month that has fewer than 3 fatal collisions is observed. Assume that the months are independent of each other.

What is the expected value for the number of months at which the first month that has fewer than 3 fatal collisionsis observed. That is, E(Y) as defined i

Answer 1

The number of vehicle fatal collisions per month is modelled here as:

The probability of having fewer than 3 fatal collisions in a month is computed here as:

Now Y here is the number of months at which the first month that has fewer than 3 fatal collisions is observed. Therefore Y is modelled here as:

Now expected value for the number of months at which the first month that has fewer than 3 fatal collisionsis observed is computed here as:

therefore 1.3070 months is the required expected months here.