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')
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.
Back to quantitative genetics!