Mike Croucher at Walking Randomly points out an interesting difference in operator precedence for several mathematical packages to evaluate a simple operation
2^3^4. It is pretty much a divide between Matlab and Excel (does the later qualify as mathematical software?) on one side with result 4096 (or
(2^3)^4) and Mathematica, R and Python on the other, resulting on 2417851639229258349412352 (or
2^(3^4)). Remember your parentheses…
Corey Chivers, aka Bayesian Biologist, uses R to help students understand the Monty Hall problem. I think a large part of the confusion to grok it stems from a convenient distraction: opening doors. The problem could be reframed as: i- you pick a door (so probability of winning the prize is 1/3) and Monty gets the other two doors (probability of winning is 2/3), ii- Monty is offering to switch all his doors for yours, so switching increases the probability of winning, iii- Monty will never open a winning door to entice the switch, so we should forget about them.
To make the point clearer, let’s imagine now that instead of 3 doors the game has 10 doors. You pick one (probability of winning 1/10) and Monty keeps 9 (probability of winning 9/10). Would you switch one door for nine? Of course! The fact that Monty will open 8 non-winning doors rather than all of his doors does not make a difference in the deal.
# Number of games and doors
n.games = 10000
n.doors = 10
# Assign prize to door for each game. Remember:
# Monty keeps all doors not chosen by player
prize.door = floor(runif(n.games, 1, n.doors + 1))
player.door = floor(runif(n.games, 1, n.doors + 1))
# If prize.door and player.door are the same
# and player does not switch
are.same = prize.door == player.door
cat('Probability of winning by not switching', sum(are.same)/n.games, '\n')
cat('Probability of winning by switching', (n.games - sum(are.same))/n.games, '\n')
Gratuitous picture: fish in New Brighton pier (Photo: Luis).
Pierre Lemieux reminds us that “a dishonest statistician is an outliar”.
If you want to make dulce de leche using condensed milk—but lack a pressure cooker—use an autoclave for 50 to 60 minutes. HT: Heidi Smith. Geeky and one needs an autoclave worth thousands of dollars, but that’s what universities are for.
Lesser and Pearl inform us that there are at least 20 modalities for making statistics fun in “Functional Fun in Statistics Teaching: Resources, Research and Recommendations”. HT: Chelsea Heaven. I’ve used music, videos, cartoons, jokes, striking examples using body parts, quotations, food, juggling, etc.
An old review of Buddhism without Beliefs: A Contemporary Guide to Awakening by Stephen Batchelor. I can’t see any statistical angle, but I liked that book.
P.S. Awesome video by OK Go HT: Eric Crampton.
Back to quantitative genetics!