Briggs I've been a pilot since 1973 and can assure you that the airport indications (ICAO, IATA) are FOUR symbols not three. The first symbol is a letter which gives the country code. Mainland US is K, Cananda is C and so on. The remaining three can be any combination of letters and numbers. And some smaller airports only use two.
No need for the gamma function in this case, we can extend the definition of n! to n=0 using (n+1)! = n! * (n + 1), setting n=0 we get 1! = 0! * 1, and 0! = 1 immediately follows
'The ontology is not the epistemology. Probability is not real. The uncertainty we have in a thing is not the thing itself, which has no uncertainty in itself! Forgetting this leads to the Deadly Sin of Reification and accounts for the large (non-DIE) errors in science.'
I have been thinking lately that a great way to see this is with a Sudoku board. Say I have 4 candidates for the number 8 in a particular 3x3 square. The probability is 1/4, the great thing about Sudoku is that it is simple enough that each candidate is obviously equally likely to be the right one, and a little hands-on play with the board will fix this in your mind. But if I obtain more evidence that eliminates 2 candidates then the probability becomes 1/2. It seems to me that developing this illustration would be a helpful way to teach this.
In the homework, you asked how many groups of 5 could be formed from those 70 elements. Is the order of the elements within each group significant? You referred to "permutations" but call them "groups", a term I generally associate with "combinations" (in which order is NOT significant).
Briggs I've been a pilot since 1973 and can assure you that the airport indications (ICAO, IATA) are FOUR symbols not three. The first symbol is a letter which gives the country code. Mainland US is K, Cananda is C and so on. The remaining three can be any combination of letters and numbers. And some smaller airports only use two.
> gamma functions
No need for the gamma function in this case, we can extend the definition of n! to n=0 using (n+1)! = n! * (n + 1), setting n=0 we get 1! = 0! * 1, and 0! = 1 immediately follows
'The ontology is not the epistemology. Probability is not real. The uncertainty we have in a thing is not the thing itself, which has no uncertainty in itself! Forgetting this leads to the Deadly Sin of Reification and accounts for the large (non-DIE) errors in science.'
I have been thinking lately that a great way to see this is with a Sudoku board. Say I have 4 candidates for the number 8 in a particular 3x3 square. The probability is 1/4, the great thing about Sudoku is that it is simple enough that each candidate is obviously equally likely to be the right one, and a little hands-on play with the board will fix this in your mind. But if I obtain more evidence that eliminates 2 candidates then the probability becomes 1/2. It seems to me that developing this illustration would be a helpful way to teach this.
All,
The link to Breaking the Law of Averages has been fixed. Apologies.
Stoves's proof is clever. Read it in your book a long time ago. I'm one of the nine.
In the homework, you asked how many groups of 5 could be formed from those 70 elements. Is the order of the elements within each group significant? You referred to "permutations" but call them "groups", a term I generally associate with "combinations" (in which order is NOT significant).
The order within a group (or permutation) does not matter.
Thanks.