What is the Expected Wheel Tax Revenue for the City in November?

[Forumite]

1. A city has 74,806 registered automobiles. Each is required to display a bumper decal showing that the owner paid an annual wheel tax of $50. By law, new decals needed to be purchased during the month of the owner’s birthday. How much wheel tax revenue can the city expect to receive in November?



2. expected value = E(X) = summation(x*f(x))
Leibnitz's rule



3. I thought there was not enough information in the problem. Can we assume that people are equally likely to be born in the different months of the year?
Anyway, all I have is E(X) = (74,506*50)*1/12
where the part in parenthesis is x and 1/12 is the probability function
(not sure).

 

[Ibix]

I think you are right that you need to assume a uniform distribution of birthdays, and I would write that assumption out explicitly.

Just one question about your answer - what is the expected revenue in (say) February?

 

[Forumite]

Going by the same approach, it would be the same answer. Did you have something else in mind?

 

[Ibix]

I think each day is equally likely...

 

[Forumite]

Ah, I see. So for November, E(X) = (74,506*50)*30/365
and for February, assuming it's not a leap year, it would be E(X) = (74,506*50)*28/365

Thanks for the help.

 

[Ibix]

That is the right answer for a non-leap year - can you figure it out for an average year?