1.
The expiration date on a credit card is given as
two digits for the month and two digits for the year. What is the expected value for the sum of the
digits in the expiration date for a credit card that expires between 01/10 and
12/15 inclusive? Assume that each month and year occur with equal frequency.

Overall there are 72 terms in the column sum of the table shown. You have to take the summation as follows:

E = 2/72 + 3/72 + 4/72 + 5/72 + ... + until 72 terms.

The easiest method is to see the trend: For the year 11, the sum column of
the table ranges from 3 to 5 and reaches a maximum of 11. For the year
12, the sum column of the table ranges from 4 to 6 and reaches a
maximum of 12 and so on. So, for each year you can find the numerators of E. Adding them and dividing by 72 gives the answer.