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Statistics portfolio page, Study notes of Mathematics

Mathematics

Learn statistics for Ap stats test

Typology: Study notes

2024/2025

Uploaded on 10/31/2025

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Unit 4B Portfolio Page: Random Variables
& Probability Distributions
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Definition of Random Variable
Discrete vs. Continuous Random Variables
Parameters of a Discrete RV
Mean:
Standard Deviation:
Combining RV Formulas
Sum of Two RV
Difference of Two RV
Linear
Transformations of
Random Variables
Add/Subtract
Multiply/Divide
Using the Calculator for
Discrete RV
Work to Show:
Mean
SD
What must be true to combine standard deviations?
Example: You have 4 apples N(4, 1.5), 3 pears N(3.5, 1),
and a basket N(25, 2). Find combined parameters.
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Mxty Mxthy
Qty Fto -
Mark a
Qie o
Mapples 4x416 Oapples1.52
x49
Mpears 3x3.5-10.5 EitiNened
Mbasket 25
M10.5 16 25 51.50 IT
64
A discrete random variable takes on a countable number of
distinct values, such as the number of students in a class. A
continuous random variable can take on any value within a
given range, like a person’s weight or height. Discrete
variables are often associated with whole numbers, while
continuous variables involve measurements that can be
infinitely precise.
Add up all possible values of x
multiplied by all the probabilities
A variable whose value
is unknown or a function
that assigns values to
each of an experiment’s
outcomes.
The mean is shifted
by the constant,
while the standard
deviation remains the
same, since there’s
no change in spread
of the data values.
The mean is scaled
by the constant, while
the standard
deviation is scaled by
the absolute value of
the constant.
When combining standard deviations, the variances are
combined, meaning that the variables must be independent and
the probability of one must not affect the other.
First, select ‘stat’ , and then select ‘edit’.
There, you can edit your list of random
variables under L1, and their corresponding
probabilities right next to their variable
under L2. Then select ‘stat’ again and go to
‘CALC’. Select ‘1-Var Stats’, and hit
calculate. You will be presented with many
information about the discrete random
variables, specifically the mean and SD.
Plug in values into the formulas.
pf2

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Download Statistics portfolio page and more Study notes Mathematics in PDF only on Docsity!

Unit 4B Portfolio Page: Random Variables

& Probability Distributions

Definition of Random Variable Discrete vs. Continuous Random Variables Parameters of a Discrete RV Mean: Standard Deviation: Combining RV Formulas Sum of Two RV Difference of Two RV Linear Transformations of Random Variables Add/Subtract Multiply/Divide Using the Calculator for Discrete RV Work to Show: Mean SD What must be true to combine standard deviations? Example: You have 4 apples N(4, 1.5), 3 pears N(3.5, 1), and a basket N(25, 2). Find combined parameters.

Mxty Mxthy

Qty Fto -

Mark a

Q ie o

Mapples 4 x^4 16 Oapples^

1.52x 4 9

Mpears 3 x3.5-10.

Eit

iNened

Mbasket 25

M 10.5 16 25 51.50 IT^6 A discrete random variable takes on a countable number of distinct values, such as the number of students in a class. A continuous random variable can take on any value within a given range, like a person’s weight or height. Discrete variables are often associated with whole numbers, while continuous variables involve measurements that can be infinitely precise. Add up all possible values of x multiplied by all the probabilities A variable whose value is unknown or a function that assigns values to each of an experiment’s outcomes. The mean is shifted by the constant, while the standard deviation remains the same, since there’s no change in spread of the data values. The mean is scaled by the constant, while the standard deviation is scaled by the absolute value of the constant. When combining standard deviations, the variances are combined, meaning that the variables must be independent and the probability of one must not affect the other. First, select ‘stat’ , and then select ‘edit’. There, you can edit your list of random variables under L1, and their corresponding probabilities right next to their variable under L2. Then select ‘stat’ again and go to ‘CALC’. Select ‘1-Var Stats’, and hit calculate. You will be presented with many information about the discrete random variables, specifically the mean and SD. Plug in values into the formulas.

Binomial Setting Binomial Probability (exactly k) Parameters of Binomial RV Mean: Standard Deviation: Binomial PDF Geometric Settings Binomial CDF Must remember: P(X≤3) P(X<3) P(X≥3) P(X>3) Work to Show Parameters of Geometric RV Mean: Standard Deviation: Calculating Geometric Probabilities Normal Approximation Condition

Binaryoutcomeeithersuccessorfailure

Independenttrialsonetrialdoesn'taffectother

Numberoftrialsissetaheadoftime

Sameprobabilityforeachtrial

P x^ k (^) E pk 1 pin

K

P probability^ of successes (^) NP 210 n^1 p (^10)

n n number of

nut (^) p of

p probability

of

K numberofsuccesses K

binomedf trials (^) p 3 binomedf trials (^) p 2 1 binomedf^ trialsp^3 Binaryoutcome^ eithersuccessorfailure 1 binomedf^ trialsp^2 Independenttrialsonetrialdoesn'taffectother

Trials until^ first^ success^ nottotal

success Sameprobability for (^) eachtrial p probabilityof success

k trialnumberof^ firstsuccess

1 p p

1b

Etnets ing

This function is used to calculate the probability of getting exactly k successes in a fixed number of trials. for example, the probability of getting exactly three heads in five coin flips. to do on a calculator, select 2nd, then vars, and find binompdf, and enter in the number of trials, the probability of success, as well as the exact number of success interested. A geometric setting occurs if you’re asking “how many trials will it take until I get my first success?” For example, what is the probability that I roll a six on the fourth roll? Or, what is the probability that I pick a queen out of the deck on the seventh pick or less? A binomial setting occurs if you’re asking, “what’s the probability of getting exactly k successes in n trials?” For example, what’s the probability of getting exactly three heads when flipping a coin five times. This is the large counts condition for probabilities, and probability distributions can only be normal when: Different combinations of k successes in n trials 1: Check the required conditions if you need to 2: Define the variables and show proper formulas for the correct random variable formula that is necessary, with filled in numbers based on the question 3: Explain calculator functions used to find the probabilities we are looking for.

  1. Interpret your responses with context based on the question. This function is used for cumulative probability which starts at zero and ends at the X value.