11 Probability Theory

Question 1

Random experiment

Answer 1

A process leading to an uncertain outcome

Question 2

Basic outcome

Answer 2

A possible outcome of a random experiment

Question 3

Sample space

Answer 3

The collection of all possible outcomes of a random experiment

Question 4

Event

Answer 4

Any subset of basic outcomes from the sample space

Question 5

Set

Answer 5

A collection of objects

Question 6

Elements

Answer 6

The objects in a set

Question 7

Mutually exclusive events

Answer 7

When A and B have no basic outcomes in common A n B =0

Question 8

Subset

Answer 8

When every element of A is also an element in B, A c B

Question 9

Collectively exhaustive

Answer 9

If the union of events completely cover the sample space

Question 10

Complement

Answer 10

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

Question 11

Probability

Answer 11

The chance that an uncertain event will occur

Question 12

Probability postulates

Answer 12

1. If A is any event in the sample space, then: 0<=P(A)<=1
2. The probability of the event A is equal to the sum of all basic outcomes of event A
3. The probability of at least one thing in the sample space will occur is P(S)=1

Question 13

Addition rule

Answer 13

P(AuB)= P(A)+P(B)-P(AnB)

Question 14

Addition rule if events A and B are collectively exhaustive

Answer 14

P(AuB)=1

Question 15

Compliment rule

Answer 15

P(Ā)=1-P(A)

Question 16

What is Conditional probability

Answer 16

The probability of one event occurring given that another event has occurred

Question 17

Equation for conditional probability of A given that B has occurred

Answer 17

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

Question 18

Equation for conditional probability of B given that A has occurred

Answer 18

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

Question 19

Multiplication rule

Answer 19

P(AnB)= P(A|B)P(B)
P(AnB)= P(B|A)P(A)

Question 20

Bayes’ theorem

Answer 20

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

Question 21

What is statistical independence?

Answer 21

Two events are statistically independent if and only if
P(AnB)=P(A)P(B)
P(A|B)=P(A)

Question 22

Probability distribution

Answer 22

Lists all the possible outcomes of a random experiment snd the probability associated with each one

Question 23

What is the probability distribution determined by

Answer 23

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