A person A is supposed to send information to a person B. The information consists of two digit numbers, including possibilities where the first digit is 0. For example 07. A is allowed to send only one two digit number to the other side. Person B is then asked to recover the two original numbers just from the received number and knowledge of the algorithm person A was using to calculate that number. (a)-Person A calculates the average of the two numbers and then send it two the person B. If the average turns not to be an integer then A rounds it upward. For example if the two numbers are 20 and 29, the average is 24.5 and A would send 25 to B. Now assume that every pair of numbers is equally likely, that is it comes with the probability of 1/10000. We define a random variable X to be the number of possibilities B has to choose from to guess the two original numbers. For example if B receives 03 then there are 13 possibilities, (00,06),(01,05),(02,04),(03,03),(04,02),(05,01),(06,00),(00,05),(01,04),(02,03),(03,02),(04,01),(0 5,00). The problem is to compute the expectation of X. (b)- Same as in (a) but now A is sending the larger of the two numbers. We define a random variable Y to be the number of possibilities B has to choose from to guess the two original numbers. For example if B receives 03 then there are only 7 possibilities, (03,00),(03,01),(03,02),(03,03),(02,03),(01,03),(00,03). Compute the expectation of Y. Comparing the expectations of X and Y which method is better. Solution 198.99.