Statistics And Probability Q3

Front 1

- way to map outcomes of statistical experiment determined by chance into a number

Back 1

Random variable

Front 2

- set whose elements are the numbers assigned to the outcomes of an experiment

- possible values of the rv x

Back 2

Sample space

Front 3

2 types of probability distribution

Back 3

Discrete and continuous random variable

Front 4

- type of probability distribution

- countable

- random variable that can take on finite number of distinct values

Back 4

Discrete rv

Front 5

- type of probability distribution

- measurable quantities

- random variable that takes on infinite, countable number of possible values , typically measurable quantities

Back 5

Continuous rv

Front 6

What type of random variable is this?

Number of heads obtained when tossing a coin 3x

Back 6

Discrete rv

Front 7

What type of probability distribution is this? Time a person can hold his or her breath

Back 7

Continuous rv

Front 8

- consists of the values a random variable can assume and the corresponding probabilities

Back 8

Discrete probability distribution

Front 9

- possible values of random variable is denoted by...

Back 9

X

Front 10

- corresponding probability of a random variable is denoted by...

Back 10

P(X) -> probability of x (event)

Front 11

- any activity whose results are unknown

Back 11

Random experiment

Front 12

- number of times an event or result of occurs

- how likely outcomes occur

- how many times x comes out

Back 12

Frequency

Front 13

- numerical quantity resulting from a random experiment

Back 13

Random variable

Front 14

- number of elements in a set

Back 14

Cardinality

Front 15

- by ratio, fraction, or decimal

- the ratio of the rv and frequency

Random variable/frequency

Back 15

Probability P(X)

Front 16

- all outcomes are equally likely to occur

- theoretical

- used in experiments (tossing a coin -> theoretical)

Back 16

Classical probability

Front 17

- uses frequency distribution

- based on observation to determine numerical probability of event

- in behavioral activity

Back 17

Empirical probability

Front 18

- assigned to an event

- based on subjective judgment, experience, info, and belief

- used for testimonies

Back 18

Subjective probability

Front 19

3 types of probability

Back 19

Classical, empirical, and subjective

Front 20

- common scale factor (common na lumalabas na outcome)

Back 20

Mass point

Front 21

How do you get the cardinality of a random experiment?

Back 21

Summation of frequency or number of events of a random experiment

Front 22

P(X=x) is read as...

Back 22

Probability of random experiment resulting to random variable

Front 23

- probability distribution of a discrete random variable described by a piece-wise function

- denoted by f(x)

Back 23

Pmf or probability mass funtion

Front 24

:if probability is in table,

:if probability is in equation,

Back 24

:Probability distribution

:Probability Mass function

Front 25

Format of mass point

Back 25

1/sum total of F or cardinality

So if total sum of F or cardinality is 12,

1/12 -> mass point

Front 26

- graphical representation of the rv on the x-axis, and the probability of the rv on the y-axis

- uses bars

- like a bar graph but does not have spaces in between bars

Back 26

Probability histogram

Front 27

- quick assessment to determine if the given rv is normally distributed

Back 27

Bell-curve or normal curve

Front 28

2 properties of a probability distribution

Back 28

1. Σ P(X) = 1 -> must be equal to 1

2. 0 ≤ P(X) ≤ 1 -> must be positive

(must satisfy both properties)

Front 29

Formula for mean

Back 29

Σ xP(X)

Front 30

Component of formula for variance

Back 30

Σ x²P(X)

Front 31

Formula for variance and standard deviation

Back 31

σ² = Σx²P(X) - μ²

σ = √(Σx²P(X) - μ²)

Front 32

Similarity and difference between mean and expected value

Back 32

Similarity: formula -> Σ xP(X)

Difference:

•mean - to interpret the data in terms of average

•expected value - to determine gains and losses in a random experiment

Front 33

In expected value, if E(x) is positive/negative...

Back 33

Positive: gain

Negative: lose

Front 34

Difference of x̄ and μ (mean)

Back 34

x̄ - used for statistics (for samples)

μ - used for parameter (for population)

Front 35

Determine the mean [Σ xP(X)], variance (Σ x²P(X) - μ²), and standard deviation √Σx²P(X) - μ²

X |10| 5 | 3 |2

P(X)|0.2|0.1|0.4|0.3

Back 35

Σ xP(X) = 4.3

Σ x²P(X) = 27.3

Σ x²P(X) - μ² = √8.81 = 2.9681

Front 36

Determine the expected value.

X | -500| 300| 500

P(X) | 0.3 | 0.5 | 0.2

Back 36

E(X) = ₱100

Front 37

- total quantity of area

Back 37

z-score

Front 38

If equation has 0,

If </>,

If ≤/≥,

Back 38

Go to z-score table

Get approximate z-score

Get the lesser/greater z-score

Front 39

If same signs,

If different signs,

Back 39

Subtract

Add

Front 40

3 characteristics of normal distribution

Back 40

1. Asymptotic

2. Symmetrical

3. Area is equal to 1 or 100%

Front 41

x -

μ -

σ -

x̄ -

s -

Back 41

x - given measurement

μ - population

σ - standard deviation

x̄ - sample data

s - sample standard deviation

Front 42

Formula if percentage was asked

Back 42

Instead of z= (x - x̄)/s

x = z(s) + x̄