11 Probability Theory Flashcards
Random experiment
A process leading to an uncertain outcome
Basic outcome
A possible outcome of a random experiment
Sample space
The collection of all possible outcomes of a random experiment
Event
Any subset of basic outcomes from the sample space
Set
A collection of objects
Elements
The objects in a set
Mutually exclusive events
When A and B have no basic outcomes in common A n B =0
Subset
When every element of A is also an element in B, A c B
Collectively exhaustive
If the union of events completely cover the sample space
Complement
The complement of an event A is the set of all basic outcomes in the sample space that don’t belong to A. Complement is denoted Ā
Probability
The chance that an uncertain event will occur
Probability postulates
- If A is any event in the sample space, then: 0<=P(A)<=1
- The probability of the event A is equal to the sum of all basic outcomes of event A
- The probability of at least one thing in the sample space will occur is P(S)=1
Addition rule
P(AuB)= P(A)+P(B)-P(AnB)
Addition rule if events A and B are collectively exhaustive
P(AuB)=1
Compliment rule
P(Ā)=1-P(A)
What is Conditional probability
The probability of one event occurring given that another event has occurred
Equation for conditional probability of A given that B has occurred
P(A|B)= P(AnB)/P(B)
Equation for conditional probability of B given that A has occurred
P(B|A)= P(AnB)/P(A)
Multiplication rule
P(AnB)= P(A|B)P(B) P(AnB)= P(B|A)P(A)
Bayes’ theorem
P(A|B)= P(B|A)P(A)/P(B)
What is statistical independence?
Two events are statistically independent if and only if
P(AnB)=P(A)P(B)
P(A|B)=P(A)
Probability distribution
Lists all the possible outcomes of a random experiment snd the probability associated with each one
What is the probability distribution determined by
The nature of the experiment not the data produced. E.g probability distribution of a coin would be 0.5 for heads and 0.5 for tails regardless of how many of each we get when we flip the coin 20 times
