##### mathematics including probability

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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.

Oct 2nd, 2015

Please see the solution below in the attached image. Please let me know if you have any questions.

Oct 2nd, 2015

The answer is correct. Thank you so much. But could you simply the last formula and explain how you got the answer 7.75.

thnx

Oct 2nd, 2015

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.

Oct 2nd, 2015

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Oct 2nd, 2015
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Oct 2nd, 2015
Dec 6th, 2016
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