Bayes Formula

Question 1

Bayes’ formula

Answer 1

a rational way to adjust viewpoints based on new information

based on the total probability rule

Question 2

Bayes’ formula formula

Answer 2

P(Event|Information) = P(Information|Event) / P(Information) * P(Event)

Question 3

Prior probabilities

Answer 3

represent the probabilities before the arrival of any new information

Question 4

The posterior probability

Answer 4

reflects the new information

Question 5

The multiplication rule of counting

Answer 5

states k tasks can be done (n1)(n2)(n3)… (nk) ways.

In this notation, the first task has n1ways of being done

Question 6

labeling

Answer 6

The number of ways n objects can be labeled with k different labels, with n1 of the first type, n2 of the second type, and so on

Question 7

multinomial formula

Answer 7

used to calculate the number of ways n objects can be labeled with k different labels, with n1 of the first type, n2 of the second type, and so on

n! / ((n1!) * (n2!) … (nk!))

Question 8

the combination formula

if K = 2

Answer 8

used if order does not matter

the number of ways r objects can be chosen from n objects is calculated using the combination formula:

nCr = (n – r) = n! / ((n - r)! * r!)

Question 9

If order does matter for a labeling problem for which k = 2, then the number of ways r objects can be chosen from n objects is calculated using the permutation formula:

Answer 9

nPr = n! / (n - r)!