Deterministic processes |
outcome can be predicted exactly in advance |
Random processes |
outcome is not known exactly (can desc the probability distribution of possible outcomes) |
Probability of event A |
0<=P(A)<=1 |
Probability of whole sample space |
P(S)=1, P(A)+P(B)+P(C) = 1 |
Event A will almost definitely not occur |
P(A)=0 |
Only small chance that event A will occur |
P(A)=0.1 |
50-50 chance that event A will occur |
P(A)=0.5 |
Strong chance that event A will occur |
P(A)=0.9 |
Event A will almost definitely occur |
P(A)=1 |
Probability successful outcome (S) |
P(S) = r/n ; r: num of successful outcomes, n: total num of equally likely outcomes |
Permutations |
Order is taken into account |
Combinations |
Order is not important |
Permutation with repetition |
n^r |
Permutation without repetition |
n!/(n-r)! |
Combination with repetition |
(r+n-1)!/r!(n-1)! |
Combination without repetition |
n!/(n-r)! |
| |
n: number of things to choose from ; r: them are chosen |
Probability events A and B both occur |
P(A∩B) |
Events A and B are mutually exclusive or disjoint cannot occur at the same time |
P{A|B}=0, P{A∩B}=0 |
Probability events A or B occur |
P(A∪B) |
Conditional probability (event A occurs, given that event B has occured) |
P(A|B) |
Independent (event A does not change the probability of event B) |
P{A|B} = P(A) |
Complement (event that not occuring) |
P(A') |
Rule of subtraction (event A will occur) |
P(A) = 1 - P(A') |
Rule of multiplication (probability of the intersection of two events) |
P(A∩B) = P(A) x P(B|A) |
Rule of addition (either event occurs, not mutually exclusive) |
P(A∪B) = P(A) + P(B) - P(A∩B) |
| |
P(A∪B) = P(A) + P(B) - (P(A) x P(B|A)) |
Random variable |
determined by a chance event, outcome of a random experiment, measurable real-valued |
Discrete random variable |
range of X is finite ot countably infinite (values X can take on, not the size of the values) |
Continuous random variable |
range of X is uncountably infinite (that makes a physical measurement) |
