Summary Formularium statistics I IBA (year 1)

STATISTICS
FÓRMULAS

, 1. Definitions of probabilities (Ch 6 &7)

1.1 General rules
P(A) always 0 < P < 1
P(A) + P(B) = 1
P(A’) =. 1 - P(A)


1.2 Operating with probabilities

A ∪ B (union)
Joint events: P(a) + P(b) - P(a b) ∩
Disjoint events: P(a) + P(b)

A ∩ B (intersection) - Both events at the same time
Independent events: P(a∩b) = P(a)*P(b) or P(A|B) = P(A)
Disjoint events: P(a∩b) = Ø - no common events


1.2.1 Rules for events

A ∩ ∪
(B ∩ ∪ (A ∩ C)
C) = (A B)
∩ ∪
(A B)’ = A’ B’
∪ ∩
(A B)’ = A’ B’
∩ ∪ ∩
A = (A B) (A B’)

1.3 Historical definitions of probability

Classical definition (equally likely)

P(A) = N(A)/N

Empirical definition (law of large numbers)

P(A) = trials(A)/t

Only if the random experiment is independently
and identically repeatable

Subjective definition - based in opinions

, 2. Counting (Ch 7 & 8)

2.1 Rules for counting
Ordering of k objects: k! = k x (k−1) x … x 2 x1

Possibilities to choose k objects from m objects

Ordered, with replacement: m^K: 4^10
Ordered, without replacement: m! /(m - k)!
Unordered, without replacement: (m)= m! / k!(m-k)!
( k)
2.2 Conditional probability
Conditional probability of event A given that event B occurs :
P(A|B) = P(A ∩ B)/ P(B)

P(A‘|B) = 1 - P(A|B)
2.2.1 Product rule
2 events

∩
P(A B) = P(B) * P(A|B) = P(A) * P(B|A)

3 events




2.2.2 Bayer’s rule

I know the outcome of the experience but I need to know the
beginning

P(A|B) = P(A) x P(A | B)/ P(B)