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205

Sep 16, 2023

3 pages

Understanding the Probability Distribution of S

user profile picture

Ahmed Nour ✓™

@ahmednour

A comprehensive guide to probability distributions and binomial probability calculations,... Show more

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 Bn,pn,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: PX=rX=r = nCr × p^r × 1p1-p^nrn-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 Psixsix=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 PRedRed=2/5 and PBlueBlue=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.

Students love us — and so will you.

4.9/5

App Store

4.8/5

Google Play

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user

 

Statistics

205

Sep 16, 2023

3 pages

Understanding the Probability Distribution of S

user profile picture

Ahmed Nour ✓™

@ahmednour

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... Show more

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

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 2: Binomial Distribution Fundamentals

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

Definition: A binomial distribution Bn,pn,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: PX=rX=r = nCr × p^r × 1p1-p^nrn-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 Psixsix=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

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

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

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

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 PRedRed=2/5 and PBlueBlue=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.

Students love us — and so will you.

4.9/5

App Store

4.8/5

Google Play

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user