Unit 6

Question 1

Probability model

Answer 1

A representation of a random event that lists all possible outcomes and their associated probabilities

Question 2

Random Variable

Answer 2

Variable that take on numeric values that describe the outcome of a chance process

Question 3

Probability Distribution

Answer 3

Of a random variable gives the possible values and probabilities

Question 4

Discrete random variable

Answer 4

Random variable that takes on a fixed list of values

Question 5

Mean (Expected Value) of a discrete random variable

Answer 5

To find mean of x, multiply each possible value of x by its probability then add all products

SEE PAGE 2

Question 6

Standard deviation

Answer 6

Measures how much the values of a random variable differ from the mean

SD of x = square root sigma (xi - M) squared x P

Use 1 var stats

SEE PAGE 4

Question 7

Tech tip

Answer 7

Use 1 var stats

Frequency list has to be the probabilities list

Question 8

AP Exam tip

Answer 8

To earn full credit you MUST show numerical values substituted for 1st few terms

Question 9

Continuous random variables

Answer 9

Can take on ANY value in an interval or range of numbers

The probability distribution of a continuous random variable is modeled by a density curve

Question 10

Adding the same positive number a to (subtracting from) each value of a random variable

Answer 10

Adds a to measures of center and location

Does NOT change measures of spread

Does NOT change shape

Question 11

Effect of multiplying/dividing a constant

Answer 11

Multiplies measures of center and location by that constant

Multiplies measures of spread by that constant

Does NOT change shape

Question 12

Linear transformations

Answer 12

If y=a + bx and x and y are random variables then

Mean of y = a + b times mean of x

This is doing 2 transformations at the same time

SEE PAGE 8

Question 13

Mean (expected value) of a sum of random variables

Answer 13

Mean sum = Mean x + y = Mean X + Mean Y

Can apply to ANY # of random variables

SEE PAGE 12

Question 14

Mean (expected value) of a difference of random variables

Answer 14

Mean Difference = Mean x - y = Mean of x - Mean of y

SEE PAGE 12

Question 15

Standard deviation of the sum/difference of two random variables

Answer 15

Sum & Difference:
SD of s squared = SD of x squared + SD of y squared

Variances add NOT SD’s

Question 16

How to calculate probability of greater or less than x

Answer 16

P(X > 7)= P(X=8) + P(X=9) + P(X=10)

Scale for Apgar score is /10

SEE PAGE 1

Question 17

How to find shape with median and mean

Answer 17

Mean = Median = Symmetric
Mean > Median = Skewed Right
Mean < Median = Skewed Left

Question 18

Binomial setting

Answer 18

When we perform “n” independent trials of the same chance process and count the # of times a “success” occurs

Question 19

Conditions for a Binomial Setting

Answer 19

B - Binary - possible outcomes placed into 1/2 categories, “success” or “failure”
I - Independent - Trials must be independent ( knowing outcome of one trial does not tell us info about next )
N - Number of Trials - Must be FIXED in advance
S - Same Probability - Prob of success must be the same on every trial

Question 20

Binomial Random Variable

Answer 20

The # of successes “x” in a binomial setting (ex. 1,2,3 … n) this is a discrete random variable

Question 21

Binomial Distribution

Answer 21

Prob dist of x in a binomial setting
Defined by 2 #’s

n= number of trials
p= prob of success

Question 22

Binomial coefficient

Answer 22

Tells us arrangement of x successes among n trials

nCx= n!/x!(n-x)

! = factorial (multiply every number below that down to one, ex. 5! =5x4x3x2x1)

Question 23

Binomial Probability Formula

Answer 23

P(x=x) =nCx (P) to the power of x
Times (1-p) to the power of n-x

n= number of trials
p= prob of success
x= # of successes

Question 24

Using calc

Answer 24

Binomialpdf - Finds the prob of exactly x successes in n trials

Binomialcdf - Finds the prob of at Most x successes in n trials

Question 25

How to find binomial probabilities

Answer 25

Step 1: State that x binomial random variable with n = ____ and p = ____ Step 2: Plan out how may successes you want and use a formula for your calculator Don’t forget: If using calc must label #’s used (like normcdf , labels are n,p,x)

Question 26

Mean and Standard Deviation If X is binomial

Answer 26

SDx = √ np(1-p) Mx = np n = number p = prob On formula sheet

Question 27

Binomial Distributions in Statistical Sampling

Answer 27

- Binomial Dists are Important in stats when we make inference about a larger population - Real world sampling like taking an SRS from a larger population population usually violates the IND condition bc it is done WITHOUT replacement - But if the pop is large enough compared to the sample we are taking, It Doesn’t Matter - Ind/10% condition: N > 10n N= pop size 10n= sample size

Question 28

Geometric setting

Answer 28

We perform independent trials of same chance process and record the # of trials it takes until we get our 1st success

Question 29

Geometric random variable

Answer 29

If x is a geometric random then x= 1,2,3,4 ….

Question 30

Geometric probability formula

Answer 30

P (X = ___ ) = (1-p) to the power of x - 1 times P ____ = trial of 1st success Prob of failure raised to # of failures On formula sheet

Question 31

Describing a geometric distribution

Answer 31

Shape: Always skewed right Center: Mx = 1/p Variability: SDx √1-p / p On formula sheet