I have, with mechanical aid, again winged my way across the globe in search of treasure. I landed disoriented and would not trust myself to calculate even the integral of the exponential function. I also cannot come up with an original post.
But since we left off with the Best Statistical Question Ever, I thought it best to confuse matters further by discussing probability distributions over counterfactual events.
Example: if a woodchuck could chuck wood, how much wood could a woodchuck chuck?
This is an unknown quantity and therefore must be represented by a probability distribution. Which distribution is the correct one? Is there only one correct one?
The first clue something is amiss is the chucking units are not given. But we can assume them: for the sake of this exercise use face cords.
A face cord, according to the site Northline Express is,
The two most common ways to measure firewood is by the “Full Cord” or “Face Cord”. You will see that our racks refer to a “Face Cord”. A face cord measures 8′ wide x 4′ high, the depth of a face cord may vary depending on the person who is cutting the wood (average firewood length is 16″-18″). A “Full Cord” of firewood measures 8′ wide x 4′ high x 4′ deep making it difficult to determine what size firewood rack to purchase since firewood is cut to different depths. Due to the confusion of calculating full cords we have decided to calculate our firewood racks by the face cord. Please check to ensure that you are purchasing the proper size firewood rack.
Your own author was responsible for creating from the raw, by hand with a fifteen-pound sledge and steel wedge, several score of face chords when he was a teen under the direction of his father. Incidentally, anybody who in the comments re-tells the old joke about the number of times wood heats you will earn permanent banishment.
But knowing the unit tells use nothing about woodchucks. Remembering that all probabilities are conditional on explicitly stated evidence, and that different evidence can lead to different probabilities, your homework is to describe the probability distribution representing the wood chucking ability of woodchucks assuming the counterfactual that woodchucks can chuck wood.
Be clear in your definitions! Best of luck. And see you when I wake up.