EXAM 1

Question 1

Descriptive Statistics

Answer 1

Pictorial and tabular methods (stem and leaf, histogram)
Numerical measures (mean, median, range, variance)

Question 2

Inferential Statistics

Answer 2

Draw conclusions about a parameter (Confidence intervals, Hypothesis testing)

Question 3

Population
Sample
Variable
Observation
Data

Answer 3

Population- a well-defined collection of objects
Sample- a subset of the population
Variable- characteristics of the objects
Observation- an observed value of a variable
Data- a collection of observations

Question 4

Variable

Answer 4

Characteristic whose value may change from one object to another in the population
Discrete (# of people in a room)
Continuous (length of a road)

Question 5

Stem and leaf plot

Answer 5

Leading value on main axis and other values on the chart
In order smallest to largest
Visualize symmetric distribution, peaks and outliers

Question 6

Dotplot

Answer 6

Represent observations with dots above the measurement
Stack dots vertically
Visualize typical values, spread of set, extremes, and gaps

Question 7

Histogram

Answer 7

When the set is large
Relative frequency over measurement
Unimodal (one peak), Bimodal (two peaks), Multimodal (many peaks), Symmetric (left=right), Pos skewed (right tail), Neg skewed (left tail)

Question 8

Relative Frequency

Answer 8

c = frequency of c / total observations

Question 9

Sample mean

Answer 9

Mean of all observations in the data set
x bar = ∑ x / n
Measures location/ center of a sample
Population mean, μ, is the average of the entire population

Question 10

Sample median

Answer 10

Middle value of the sample, x~
Order from small to large and find middle value
Average the value if there are two middle values
Population median, μ

Question 11

Trimmed mean

Answer 11

A method used to make the mean less skewed due to outliers by removing a percent of the top and lower values

Question 12

Quartiles

Answer 12

Median separates the sample into lower and upper sub-samples
Q1 is median of lower half 
Q2 is median
Q3 is the median of the upper half 
IQR = Q3-Q1

Question 13

Variance

Answer 13

Average magnitude of the devition from the sample mean

s^2 = (∑ xi - x bar) ^2 / n-1

Question 14

Standard Deviation

Answer 14

s = sqrt(s^2)

Square root of variance

Question 15

Degree of Freedom

Answer 15

n-1

Question 16

Sxx

Answer 16

Numerator of s^2
Sxx = ∑ (xi - xbar)^2
Sxx = ∑ xi^2 - [ (∑ xi)^2 / n ]

Question 17

Boxplots

Answer 17

Five number summary (min, Q1, x~, Q3, max)
Center, spread, symmetry, outliers
1. Draw horizontal axis find Q1, Q2, Q3, and IQR
2. Place a rectangle above the axis with the Q1 and Q3
3. Place a vert line on Q2
4. Draw wiskers to largest and smallest point

Question 18

Experiment

Answer 18

Any activity or process whose outcome is subject to uncertainty

Question 19

Sample space

Answer 19

the set of all possible outcomes of that experiment, S

Question 20

Event

Answer 20

Any collection or subset of outcomes contained in the sample space S
Use upper case letters to denote events
Simple: One outcome
Compund: More than one outcome

Question 21

Complement

Answer 21

A’

all outcomes of S that are not in A

Question 22

Union

Answer 22

A ∪ B

All outcomes that are either in A or B or in both events

Question 23

Intersection

Answer 23

A ∩ B

All outcomes that are in both A and B

Question 24

Empty Set

Answer 24

The null event
No outcomes
“∅”

Question 25

Mutually Exclusive or Disjoint

Answer 25

A and B have not outcomes in common | A ∩ B = ∅

Question 26

Probability

Answer 26

Measure of the chance that A will occur

Question 27

Axioms

Answer 27

P(A) ≥ 0 P(A) ≤ 1 P(S) = 1

Question 28

Interpreting relative frequency

Answer 28

Rel Freq varies at low number of times | Will approach the limiting rel freq after many times

Question 29

Complement Law

Answer 29

P(A) = 1 − P(A′)

Question 30

Addition Law

Answer 30

P (A∪B) = P (A) + P (B) − P (A∩B) Mutually Exclusive: P (A∪B) = P (A) + P (B) P (A∪B∪C) = sum of individual - double intersections - all intersection

Question 31

Equally likely outcome

Answer 31

Fair coin, fair die p = 1/N N = # of outcomes

Question 32

Equally likely multiple outcomes

Answer 32

``` p = N(A) / N N = # of possible outcomes N(A) = # of outcomes in question, A ```

Question 33

Product rule for ordered pairs

Answer 33

Number of possible pairs = n1 * n2 | n = # of possible options

Question 34

Permutations

Answer 34

An ordered subset | P k,n = n! / (n−k)!

Question 35

Combination

Answer 35

An unordered subset | C k,n = n! / (n−k)! * k!

Question 36

Conditional Probability

Answer 36

Probability of A given B had occured | P (A|B) = P (A ∩ B) / P (B)

Question 37

Multiplication Rule with cond prob

Answer 37

P (A ∩ B) = P (A|B) P (B) = P (B|A) P (A)

Question 38

Bayes' Theorem / Law of total probability

Answer 38

P(B) = ∑ P(B | Ai) P(Ai)

Question 39

Independence

Answer 39

Two events A and B are independent if P (A|B) = P (A), and are dependent otherwise

Question 40

Multiplicative rule when independent

Answer 40

P (A ∩ B) = P(A) * P(B)

Question 41

Random variable

Answer 41

Any rule that associates a number with each outcome in S | Upper case letters

Question 42

Bernoulli random variable

Answer 42

Any random variable whose only possible values are 0 and 1

Question 43

Discrete vs Continuous

Answer 43

``` Discrete = countable, number of something, whole numbers Continuous = possible values consists of every number in a range, many decimals, probability = 0 ```

Question 44

Probability mass function (discrete)

Answer 44

Distribution of all the probabilities For every possible value of x of the random variable, the pmf specifies the probability of observing that value when the experiment is performed.

Question 45

Cumulative distribution function

Answer 45

Method to describe the distribution of probability by finding the probability if x is greater than or equal to Creates a step function

Question 46

Cumulative Distribution Equation

Answer 46

P(a ≤X ≤b) = F(b) −F(a−)

Question 47

Expected Value

Answer 47

E(X) = μx = ∑ x ·p(x) = sample mean E(X^2) = ∑ x^2 ·p(x) = expectation squared

Question 48

Expectation Variance

Answer 48

V (X) = ∑ (x −μ)^2 ·p(x) = E[(X −μ)2] SD = sqrt( E[(X −μ)2] ) alt. E[(X −μ)2] = E(x^2) - [E(x)]^2

Question 49

Variance of Linear Function

Answer 49

V (aX + b) = σ^2 (aX+b) = a^2 σ^2 X and σ aX+b = |a|σ X

Question 50

Binomial Distribution

Answer 50

An experiment where trials are independent and can take on either success or failure. P = C 5,x / N b(x;n,p) = n,x p^x (1-p)^(n-x) E(X) = np V (X) = np(1 −p) σX = √np(1 −p)