Units 12-16

Question 1

TRIAL

Answer 1

Occasion where random phenomena are observed

Question 2

OUTCOME

Answer 2

Result of random phenomena noted at the end of a trial

Question 3

EVENT

Answer 3

Combination of multiple outcomes

Question 4

SAMPLE SPACE

Answer 4

List of all possible outcomes

Question 5

How is sample space notated

Answer 5

S = {outcome, outcome, outcome…}

Question 6

NONEXISTENT LAW OF AVERAGES/GAMBLER’S FALLACY

Answer 6

Belief that an outcome that hasn’t appeared in many trials is “due”

Question 7

LAW OF LARGE NUMBERS

Answer 7

In the long term, after many trials, the mean will settle on one number

Question 8

CONDITIONS OF LLN:

Answer 8

Outcomes must have the same probability for each trial, and events must be independent

Question 9

EMPIRICAL PROBABILITY

Answer 9

The probability found after repeating a trial many times (LLN)

Question 10

DISJOINT

Answer 10

Two events that cannot exist simultaneously

Question 11

INDEPENDENT

Answer 11

Two events that don’t effect each other

Question 12

THEORETICAL PROBABILITY

Answer 12

Probability determined by a model

Question 13

How is probability notated?

Answer 13

P(outcome)

Question 14

What is the formula for probability when every event is equally likely?

Answer 14

P(A) = #of outcomes A/# of total possible outcomes

Question 15

PROBABILITY ASSIGNMENT RULE

Answer 15

Set of all possible outcomes must equal 1

Question 16

COMPLEMENT

Answer 16

The probability of an event not happening. Is equal to 1 - P(A)

Question 17

ADDITION RULE

Answer 17

P(A or B) = P(A) + P(B) only if events are disjoint

Question 18

MULTIPLICATION RULE

Answer 18

P(A and B) = P(A)*P(B) only if events are independent

Question 19

GENERAL ADDITION RULE

Answer 19

P(A or B) = P(A) + P(B) - P(A and B)

Question 20

GENERAL MULTIPLICATION RULE

Answer 20

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

Question 21

CONDITIONAL PROBABILITY

Answer 21

Probability outcome will be B given we have chosen variable A

Question 22

How is conditional probability notated?

Answer 22

P(B|A)

Question 23

TREE DIAGRAM

Answer 23

Shows conditional probability and compares more than 2 groups

Question 24

Does P(B|A) = P(A|B)

Answer 24

No, you have to redo the problem

Question 25

How do you find EXPECTED VALUE

Answer 25

the sum of (x*P(X = x))

Question 26

How is expected value notated?

Answer 26

E(X)

Question 27

How do you find standard deviation of a random variable?

Question 28

What happens to the expected value and standard deviation when data is shifted

Answer 28

Expected value is shifted, SD is unaffected

Question 29

What happens to the expected value and standard deviation when data is rescaled

Answer 29

Expected value and variance are rescaled

Question 30

What is E(X plus or minus Y)

Answer 30

E(X) plus or minus E(Y)

Question 31

What is Var(X plus or minus Y)

Answer 31

Var(X) + Var(Y)

Question 32

DISCRETE VARIABLES

Answer 32

Variables that have a finite set of outcomes

Question 33

CONTINUOUS VARIABLES

Answer 33

Outcomes can be any number

Question 34

NORMAL VARIABLES

Answer 34

Variables that can be approximated with the normal distribution

Question 35

BERNOULLI TRIALS

Answer 35

Trials that are:
Success/fail
Probability of one does not affect the other

Question 36

How is P(success) noted in Bernoulli trials?

Answer 36

p

Question 37

GEOMETRIC PROBABILITY MODEL

Answer 37

P(X=x) = (q^(x-1))*p

Question 38

What does P(X = x) mean in the geometric probability model?

Answer 38

Probability that it will take x trials to reach success

Question 39

How is the geometric probability model notated

Answer 39

Geom(p)

Question 40

What is the expected value in the geometric probability model

Answer 40

1/p

Question 41

What is the variance in the geometric probability model

Answer 41

q/(p^2)

Question 42

BINOMIAL MODEL

Answer 42

(nCk)(p^k)(q^(n-k))

Question 43

What is nCk in the binomial model

Answer 43

Total number of combinations resulting in n successes
equals n!/(k!(n-k)!)

Question 44

What is k in the binomial model

Answer 44

Number of successes

Question 45

When can we use the normal model to approximate the binomial model?

Answer 45

np>10, nq>10