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Probability, Random Variables, and Probability Distributions

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The Binomial Distribution

Understanding the Probability Distribution of S

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Understanding the Probability Distribution of S
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Ahmed Nour ✓™

@ahmednour

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414 Followers

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A comprehensive guide to probability distributions and binomial probability calculations, focusing on discrete random variables and practical applications.

  • The guide covers fundamental concepts of probability distribution of a random variable S through spinner and dice examples
  • Detailed explanations of binomial distribution assumptions for modeling including success/failure trials and independence
  • Step-by-step methods to calculate cumulative binomial probability using calculator functions
  • Real-world applications including radio listener statistics and dice roll experiments
  • Practical examples demonstrating probability calculations for various scenarios

9/16/2023

172

Probability Distributions random variable i'S sumple space १८ 1 2 3 4 56 P(X=x) 1/6 1/6 1/6 1/16 1 x 1 P(SS) 26 This spinner is spun until i

View

Page 2: Binomial Distribution Fundamentals

This page explores the binomial distribution and its applications in probability calculations.

Definition: A binomial distribution B(n,p) models the number of successes in n independent trials, each with probability p of success.

The key components covered include:

  • Probability mass function formula: P(X=r) = nCr × p^r × (1-p)^(n-r)
  • Cumulative probability calculations
  • Calculator methods for binomial probabilities

Highlight: The binomial distribution requires:

  • Fixed number of trials
  • Independent events
  • Constant probability of success

Example: A biased dice with P(six)=0.3 rolled 15 times, calculating probability of exactly 4 sixes.

Probability Distributions random variable i'S sumple space १८ 1 2 3 4 56 P(X=x) 1/6 1/6 1/6 1/16 1 x 1 P(SS) 26 This spinner is spun until i

View

Page 3: Advanced Binomial Applications

This page applies binomial distribution concepts to real-world scenarios and complex probability calculations.

Example: Analysis of radio listeners where 30% of residents listen to local radio, sampling 10 residents randomly.

The page covers:

  • Determining appropriate distribution models
  • Calculating probabilities for at least/at most scenarios
  • Finding threshold values for specific probability conditions

Highlight: When solving for threshold values, systematic testing of values is required to find the solution that satisfies the given condition.

Vocabulary: Cumulative probability - The probability that a random variable takes a value less than or equal to a specified value.

Probability Distributions random variable i'S sumple space १८ 1 2 3 4 56 P(X=x) 1/6 1/6 1/6 1/16 1 x 1 P(SS) 26 This spinner is spun until i

View

Page 1: Probability Distributions and Random Variables

This page introduces fundamental concepts of probability distributions through practical examples using spinners and dice.

Definition: A probability distribution shows all possible values of a random variable and their associated probabilities.

Example: A spinner experiment where P(Red)=2/5 and P(Blue)=3/5, spun until red appears or four total spins occur.

Vocabulary: Discrete random variable - A variable that can only take specific, countable values.

The page demonstrates probability calculations for various scenarios including:

  • Discrete uniform distributions with values from 1 to 50
  • Probability calculations for specific values and ranges
  • Multiple-spin probability calculations using tree diagrams

Highlight: For a discrete uniform distribution, each possible outcome has an equal probability of occurring.

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

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Knowunity is the # 1 ranked education app in five European countries

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Subjects

/

Statistics

/

Probability, Random Variables, and Probability Distributions

/

The Binomial Distribution

Understanding the Probability Distribution of S

user profile picture

Ahmed Nour ✓™

@ahmednour

·

414 Followers

Follow

A comprehensive guide to probability distributions and binomial probability calculations, focusing on discrete random variables and practical applications.

  • The guide covers fundamental concepts of probability distribution of a random variable S through spinner and dice examples
  • Detailed explanations of binomial distribution assumptions for modeling including success/failure trials and independence
  • Step-by-step methods to calculate cumulative binomial probability using calculator functions
  • Real-world applications including radio listener statistics and dice roll experiments
  • Practical examples demonstrating probability calculations for various scenarios

9/16/2023

172

 

11th/12th

 

Statistics

1

Probability Distributions random variable i'S sumple space १८ 1 2 3 4 56 P(X=x) 1/6 1/6 1/6 1/16 1 x 1 P(SS) 26 This spinner is spun until i

Page 2: Binomial Distribution Fundamentals

This page explores the binomial distribution and its applications in probability calculations.

Definition: A binomial distribution B(n,p) models the number of successes in n independent trials, each with probability p of success.

The key components covered include:

  • Probability mass function formula: P(X=r) = nCr × p^r × (1-p)^(n-r)
  • Cumulative probability calculations
  • Calculator methods for binomial probabilities

Highlight: The binomial distribution requires:

  • Fixed number of trials
  • Independent events
  • Constant probability of success

Example: A biased dice with P(six)=0.3 rolled 15 times, calculating probability of exactly 4 sixes.

Probability Distributions random variable i'S sumple space १८ 1 2 3 4 56 P(X=x) 1/6 1/6 1/6 1/16 1 x 1 P(SS) 26 This spinner is spun until i

Page 3: Advanced Binomial Applications

This page applies binomial distribution concepts to real-world scenarios and complex probability calculations.

Example: Analysis of radio listeners where 30% of residents listen to local radio, sampling 10 residents randomly.

The page covers:

  • Determining appropriate distribution models
  • Calculating probabilities for at least/at most scenarios
  • Finding threshold values for specific probability conditions

Highlight: When solving for threshold values, systematic testing of values is required to find the solution that satisfies the given condition.

Vocabulary: Cumulative probability - The probability that a random variable takes a value less than or equal to a specified value.

Probability Distributions random variable i'S sumple space १८ 1 2 3 4 56 P(X=x) 1/6 1/6 1/6 1/16 1 x 1 P(SS) 26 This spinner is spun until i

Page 1: Probability Distributions and Random Variables

This page introduces fundamental concepts of probability distributions through practical examples using spinners and dice.

Definition: A probability distribution shows all possible values of a random variable and their associated probabilities.

Example: A spinner experiment where P(Red)=2/5 and P(Blue)=3/5, spun until red appears or four total spins occur.

Vocabulary: Discrete random variable - A variable that can only take specific, countable values.

The page demonstrates probability calculations for various scenarios including:

  • Discrete uniform distributions with values from 1 to 50
  • Probability calculations for specific values and ranges
  • Multiple-spin probability calculations using tree diagrams

Highlight: For a discrete uniform distribution, each possible outcome has an equal probability of occurring.

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying