Problem Solving

Describe your methods in detail, using
equations/illustrations/graphs as needed. Each response should take
no more than two pages and should be submitted as a printed
document.
Don’t forget to include a new question of your own for consideration on
future HWs and class discussions.

  1. In a class of 50 students and 1 professor (i.e. this class), what is the
    probability that at least two people share the same birthday? What
    about at least three people? While you can probably show this fairly
    easily using logic and math, verify the results using random number
    generation and a sufficient number of loop iterations. We will
    “experimentally” check in class!
  2. 5000 kg/h of a 50:50 (kg:kg) of a pressurized liquid feed (F) of
    hexane and octane at 90oC and 5 atm is to be distilled. The distillate (D)
    is 91 mol% hexane and the bottoms product (B) is 88 mol% octane.
    Using matrix operations, solve for the outlet flowrates in kmol/h.
  3. Using data from the Saban era of Alabama football (excluding
    current season), gather the requisite data and fit the following to the
    appropriate type of statistical distribution (Normal or Poisson) using
    Matlab and report the mean and other relevant terms. Present a graph
    for each.
    • Losses per season (including playoffs)
    • Team rushing yards per game
    • Team passing touchdowns per game
  4. A mysterious man in a trench coat approaches you and pulls out an
    envelope. He says that it contains a random amount between $1 and
    $1000. If you can guess the exact amount, you can keep the money.
    After each guess, you will only be told if it is too high or too low.
    However, you only get 9 tries. Using Matlab code, “play” this game
    25,000 times (or more!). What were your average winnings? Is there
    an “ideal” first guess that results in more wins?