Hey, what's your size?

Recently, Stew emailed Uncle Kermit the following question: "If you were a t-shirt to be worn by yourself, what size t-shirt would you be?" I'm not sure where Stew is going with this line of questioning, but me thinks he has something along the lines of an "I'm with Stupid" t-shirt. Each New Year's, we share a cabin with a few friends (and dogs), and it's become somewhat of a tradition for folks to bring gag gifts to the cabin that are typically used as door prizes for various games of chance and/or skill the humanoids participate in until the wee hours of the morning. Stew's been in training for a couple weeks. I've been finding him out in the garage practicing his tabletop shuffleboard stroke. There's a traveling trophy at stake, and our house has yet to win a trophy to display on our fireplace mantel (or for Stew to keep under his pillow out of fear Aunt Veronica might come steal it if he ever wins one... she's a vicious competitor).

Anyway, following is Uncle Kermit's response to the t-shirt question that we found intriguing enough to share with y'all:

Assume a train leaves Chicago at 10:10AM traveling due east at 75MPH, while a second train leaves New York at 12:00PM traveling due west - on the same track - at a speed of 110MPH.

The eastbound train is loaded with Vienna beef, Chicago-style hot dogs on poppy-seed buns with mustard, tomato, and sport-peppers. The westbound train is carrying New York strips grilled medium-rare topped with mushrooms and served with broccoli covered in a rich hollandaise sauce.

Assume I am sitting in Philadelphia eating cheese-steak sandwiches when the two trains collide in front of me, spilling their contents. Furthermore, assume I stop eating my sandwich and begin to eat the food which has spilled in front of me.

The act of picking up a hotdog or a steak constitutes a random variable which follows the discrete, Bernoulli probability distribution.

Assume a stochastic vector of:
Food-item (X) = {.33 - steak} {.67 - hotdog}

If a steak has 2.34 times the number of calories as a hotdog, and I am able to eat continuously for 15 minutes before rescue workers force me to leave the scene of the accident, determine the number of calories (denoted by variable "C" and expressed in units of whole hotdogs) that will be consumed by me.

If C is less than or equal to 4, then I am a Large.
If C is greater than 4 but less than 8, then I am an X-Large.
If C is greater than or equal to 8, then I am fatter than I think.
Note: Express all numbers to the 3rd significant digit and show your work.

Cheers,
--kermit

Now, I wouldn't call Uncle Kermit a nerd, but he is some sort of engineer (and not the kind that drives a train, despite the use of locomotives in the above story problem). Plus, his hero is supposedly Steve Urkel. Did I say thaaaat? If you are also an Urkel fan, then you will undoubtedly understand the comedic brilliance of my inserting the aforementioned Urkel phrase.

Anyway, Stew was going to assign this problem to Momma, but then he remembered how much trouble she had with her math homework while she was getting her Masters in Public Health (MPH) degree a few years ago. We often found her sitting at the kitchen table at night with her Statistics book open while she plucked at her eyebrows with both hands as she rocked back-and-forth in her chair. Luckily, Stew was a math genius in his younger years, so he was always there for Momma with a supportive, "Linda, the Fiducial Method is an attempt to measure the precision of a statistical estimate. Fiducial intervals are an alternative to confidence intervals; however, they haven't been free from controversy. Basically, their meaning has not been universally accepted. If you can't grasp this theorem, then I can't really help you. So, I'm going downstairs to watch Law & Order."

But, since Stew says Uncle Kermit's riddle is over his head, the burden of solving it has been turned over to me. Therefore, I will solve it for you here:

Firstoff, there are many famous open problems in mathematics, many dating back hundreds of years. For instance, the Riemann hypothesis (from 1859) and Goldbach's conjecture (1742). And, you need to realize that we mathematicians are typically interested not in calculating, but in finding and describing patterns (or creating proofs that justify a theorem mathematically). Thusly, my research has determined that Uncle Kermit has a long established pattern of spewing bullshit, both verbally and in written form. And, I'm assuming outdoor temperatures in Philadelphia at the time of the hypothetical accident will not exceed 45 degrees Fahrenheit, therefore, the egg-based hollandaise sauce topping the New York strip beef should not be adversely affected to the point of causing Kermit to vomit, and his horseshoe mustache should remain fairly free of debris. Appending my assumptions into the pattern of Kermit's long history of bullshitting, the answer to his story problem is 6.50. Or, he would be an XL t-shirt. A portion of my work can be found here. However, since a proof is a logical argument, as opposed to an empirical one, there is not enough chalk in the world - nor a blackboard large enough - to show a proof of Kermit's bullshit pattern. So, you're just going to have to take my word for it. Kermit is an XL, not to mention strikingly handsome. I love you Uncle Kermit!