By signing, I certify that the only materials I used to complete this exam (besides paper, writing implement, and hand-held calculator) were my course text book, my course notes, my homework and homework assignments, my in-class exercises and my computer exercises. I also certify that the only internet resource I used for this exam was our course web-site. I finally certify that the only person I consulted in any way on this exam was the instructor of record for this course, Krishna Chowdary. I also agree not to discuss this exam in any way with any person until after the exam due date.
1. (7 points) Please choose ONE of the following questions to answer. Please indicate clearly which question you are answering.
(i) You flip a coin 1000 times. Determine the probability of getting 600 heads and 400 tails. Express your answer in the form , where is some number and is some integer. You will likely need to use Stirling’s approximation, but you’ll need to use your best judgment as to which version is most appropriate. (Note that the math here is the same as the math we would do for a two-state system).