Probability 2

Question 1

Random process

Answer 1

We know what outcomes could happen but don’t know which one will happen

Question 2

probability 0 >=P<=1
Frequentist interpretation
Bayesian interpretation

Answer 2

Frequentist: probability measures the frequency of various outcomes of a random process an infinite number of times.
Bayesian: each value has its own probability of becoming true

Question 3

Law of large numbers

Answer 3

more observations cause the proportion of the outcome to = the probability

Question 4

gambler’s fallacy/law of averages

Answer 4

think they are due for a win because of Law of large numbers

Question 5

Disjointed outcomes

Answer 5

Cannot happen at the same time

Question 6

Non-Disjointed outcomes

Answer 6

Can happen at the same time

Question 7

set
element
subset
complement
union
intersection
empty set
Disjoint
Difference

Answer 7

set-the large area S
element-a value in a set
subset-set A is fully in S
complement= S-A
union=A+B
intersection=A,B overlap
empty set=no elements
Disjoint= intersection between non-overlapping sets
Difference= A-B elements in a that are not in B

Question 8

Probability Distribution
and rules (3)

Answer 8

A table stating the probability of outcomes.

1. ) events must be disjointed.
2. ) probabilities are between 0 and 1
3. ) total up to 1

Question 9

Experiment, Sample space, Event, Probability function, Discrete sample space

Answer 9

Experiment- repeatable procedure with well defined possible outcomes
Sample space-the set of all possible outcomes
Event- a subset of the sample space/collection of outcomes
Probability function- a function giving probability to each outcome
Discrete sample space- a list-able sample space finite or infinite

Question 10

The probability function

Answer 10

P assigns w a probability P(w).

• has to be within 0-1
• sum of all possible outcomes =1

Question 11

Rules of Probability 3

Answer 11

P(S-A)=1-P(A)

• if A and B are -disjointed P(A or B)= P(A)+P(B)
• non disjointed p(A or B)= P(A)+P(B)-P(A and B)

Question 12

Process independence

Answer 12

Independent if knowing the outcome of one does not give info about the other

Question 13

Marginal Probability

Answer 13

Chance of one event Occurring

Question 14

Joint Probability

Answer 14

Chance of two events Occurring

Question 15

Conditional Probability

Answer 15

Chance of outcome Occurring if one outcome is already known P(A|B)=P(A+B)/B

Question 16

multiplication of dependent variables

Answer 16

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

Question 17

Independence Math

Answer 17

If A is independent

P(A|B)=P(A)

Question 18

Law of total probability

subset A is equally apart of 3 equal subsets B1-3

Answer 18

P(A)=P(A and B1)…

P(A)=P(A|B1)P(B1)..

Question 19

Bayes theorem

Answer 19

I cant