Solo Practice. Binomial Distribution Examples, Problems and Formula Mean and Variance of Binomial Distribution. I'm doing some practical work on the binomial distribution but currently finding it difficult to answer iii-c. To learn more, see our tips on writing great answers. \(\require{color} \displaystyle \) $$ (1 + … - Total 20 Questions on Binomial Theorem with Answers. The basic binomial expansion that we use in mathematics is {eq}(1+x)^n = nC0 x^0+nC1 x^1+nC2 x^2+ \cdots +nCnx^n {/eq}. Students should also have a picture of what a binomial distribution looks like. Active 4 years, 7 months ago. Chapter 5 Binomial Distribution 99 5 BINOMIAL DISTRIBUTION Objectives After studying this chapter you should • be able to recognise when to use the binomial distribution; • understand how to find the mean and variance of the distribution; • be able to apply the binomial distribution to a variety of problems. Binomial Distribution DRAFT. Basic and advanced math exercises on binomial theorem. Integral also contains many interactive resources which are designed to be used on screen. NEET; Daily Practice Sheets ; JEE Main; Binomial Theorem Class 11 MCQ Sheet 1. • Answer all questions and ensure that your answers to … How do snakes determine the direction of prey from their thermal infrared sensing pit organs? Starter activity: Shut your notebook and textbook and write on the whiteboard: 1. when a random variable follows the binomial distribution 2. what B(n,p) means 3. what the formula is for the probability of r successes in n trials when the probability of success in each trial is p Our maths education specialists have considerable classroom experience and deep expertise in the teaching and learning of maths. Binomial distribution experiment. the binomial theorem mc-TY-pascal-2009-1.1 A binomial expression is the sum, or difference, of two terms. About the Book Author. the mean value of the binomial distribution) is. Oxford PAT (edexcel student) and Alevel Maths. A binomial Distribution can be defined as when a random variable X that counts the number of successes, k, in the n trials is said to have a binomial distribution with parameters. Here is the full question and the answers I've provided. For Enquiry. Assuming that a student who guesses at the answer will be correct with probability {tex}\frac{1}{4}{/tex}. Binomial distribution probability help please math? If the definite integral is used, then it is important to set the upper and lower limits. To play this quiz, please … In general a Binomial distribution arises when we have the following 4 conditions-identical trials, e.g. Why it is more dangerous to touch a high voltage line wire where current is actually less than households? See more ideas about binomial distribution, math formulas, math tricks. Each test is 32 marks, and is split into two sections. For further samples and more information please visit www.integralmaths.org . Please note that all tutorials listed in orange are ... A short student test with answers. Casio FX-85ES - how to change answers to decimal? 5.2 The Poisson distribution • The binomial distribution is about counting successes in a fixed number of well-defined trials, ie n is known and fixed. NCERT Solutions for Class 12 Maths Chapter 6 Applications of Derivatives will not just help you to prepare for your Class 12 board exams but also strengthen your JEE preparation. If this claim is true, what is the probability that: Made by expert teachers. Venn diagrams matching task. 1. ... Statistical calculations task. Alan Anderson, PhD is a teacher of finance, economics, statistics, and math at Fordham and Fairfield universities as well as at Manhattanville and Purchase colleges. RD Sharma solutions for Class 12 Maths chapter 33 (Binomial Distribution) include all questions with solution and detail explanation. n and p, written bin(k; n, p). 1800-212-7858 / 9372462318. Asking for help, clarification, or responding to other answers. P(X=r) will be maximum when r is the mode. Let {tex}\frac{3}{4}{/tex} be the probability that he knows the answer and {tex}\frac{1}{4}{/tex} be the probability that he guesses. 3 years ago. Finish Editing. 4.3 3 customer reviews. View binomial ans.pdf from ECON 288 at Jinnah Institute of Management Sciences, Layyah. [4] 3. Edexcel A Level Statistics & Mechanics exam revision with questions and model answers for Approximating The Binomial Distribution 1. Binomial theorem. MCQs for NEET, JEE and All Competetions. Given an exact formula, how can Mathematica find a probability distribution whose PDF matches it? Use MathJax to format equations. And here is how we write the answer: Plus C. We wrote the answer as x 2 but why + C? Binomial integral: Integral of the form: is called the binomial integral where, a and b are real numbers while m, n and p are rational numbers. The binomial distribution is a discrete one. How to show that Bell states are orthonormal, Reason for non-powered superheroes to not have guns. Q. Clumsy clive on probability trees. Integral maths - functions end of topic test answers? Preview. For example, x+1, 3x+2y, a− b are all binomial expressions. [2019 Updated] IB Maths SL Questionbank > The Binomial Theorem. I provided water bottle to my opponent, he drank it then lost on time due to the need of using bathroom. Determine the value of n. x , n = 21 . Complete and customized answers for each question in RD Sharma Mathematics; Detailed explanation for each question; Chapter-wise RD Sharma Solutions Class 12 Maths. The Binomial Distribution and Hypothesis Testing Instructions • Use black ink or ball-point pen. It is the "Constant of Integration". Contact. Mathematics. Find your group chat here >>. Integrating Binomial Expansion is being used for evaluating certain series or expansions by substituting particular values after integrating binomial expansion. Homework. Prove that $$ n\binom{n}{k}\int_{0}^{\frac{k}{n+1}}t^k(1-t)^{n-k}\,dt \le 1/2. 1 of 3 NT 24/04/17 Version 1.4 The Binomial Expansion (AS) D1 [Understand and use the binomial expansion of na bx for positive integer n; the notations n! Binomial … The Given Binomial distribution has parameters, n= 100 and p= 1/3. The discrete random variable X has binomial distribution B ,(n p). Questions have been taken from the 2008 edexcel a-level mathematics specification and are suitable for the new 2017 specification. Clumsy clive on probability trees. variables with any distribution? AS/Year 1 Binomial Expansion - Edexcel Past Paper Questions. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE. Integral has been developed by experts at MEI. 1. AQA GeoGebra Tasks for AS Core - The factor theorem . Active 2 years, 8 … Share practice link. You're welcome. There are similar tests on Integral for all topics and students can enter their answers online for immediate feedback. by jpfeil. distribution; • be able to apply the binomial distribution to a variety of problems. Questions from answers. Welcome to advancedhighermaths.co.uk A sound understanding of the Binomial Theorem is essential to ensure exam success. Estimate parameters of a derived distribution. Is there a G-test equivalent for continuous variables? What is the probability that if 25 such tubes are tested 1. Estimate of incomplete binomial integral. Solution for Find the numeric value ( in terms of c ) for the following definite integral analytically by (a) Integration by Parts (b) Using properties and… Introducing the binomial distribution through a dice experiment. Save. Tell us a little about yourself to get started. Become our. There are two cases for mode of binomial distribution: Case 1: If (n+1)/p is an integer the Binomial distribution is bi modal and the two modal values are (n+1)/p and (n+1)/p - 1. I did not get the expected result of $1$ when I tried to integrate the binomial distribution in different ways (v10.0): Btw: Welcome to Mathematica.StackExchange! 10:00 AM to 7:00 PM IST all days. Equation of tangent to circle- HELP URGENTLY NEEDED, Tips on passing Functional skills Maths level 2, MathsWatch marking answers as wrong when they are clearly correct, Integral Maths Topic Assessment Solutions, Oxbridge Maths Interview Questions - Daily Rep. Stop my calculator showing fractions as answers? CBSE Topper Answer Sheet; CBSE Sample Papers for Class 12; CBSE Sample Papers for Class 11; CBSE Sample Papers for Class 10; CBSE Sample Papers for Class 9; CBSE Sample Papers Class 8; CBSE Sample Papers Class 7; CBSE Sample Papers Class 6; Textbook Solutions. I did not get the expected result of $1$ when I tried to integrate the binomial distribution in different ways (v10.0): expected: $\frac{1}{n \choose k} = \frac{k! Statistical calculations task. Need assistance? Fastest query to filter product by countries. Topic tests can be used alongside our Route Maps to help your track student progression as you teach the specification content.. Each test is 32 marks, and is split into two sections. After the Integral Symbol we put the function we want to find the integral of (called the Integrand), and then finish with dx to mean the slices go in the x direction (and approach zero in width). 1 $\begingroup$ Let $0\le k \le n$. = \frac{\Gamma(k + 1) \Gamma(n - k + 1)}{\Gamma[n + 1]}$ AQA … Makox MCQs. You may delete the question if it's too embarrassing for you. This video has not been made yet. Or can anyone help me with these questions please? In this chapter, our Maths experts will support you to revise concepts such as maxima, minima, approximation, rate of change, etc. - my answer: 0.1535 3. They can also be used for AQA and OCR. Edit. Academic Partner. I confused the parameter and the variable of a distribution. Can we get to 10,000 posts before 2021 begins and WIN PRIZES? This quiz is incomplete! What is the probability that the student knows the answer given that he answered it correctly? B 1 for mean only Special case for parts a and b If they use 0.1 do not treat as misread as it makes It easier. Think WriTe a 1 Check that all the characteristics have been satisfied for a binomial distribution. The mean of X is three time as large as the standard deviation of X. Probability diagrams. Here's the question I'm stuck on: We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out. Note: Statistical tables can be found in many books and are also available online. Get Free NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem. Delete Quiz. How critical is it to declare the manufacturer part number for a component within the BOM? Hi, any help is much appreciated. If a random variable X has a binomial distribution, we write X ~ B(n, p) (~ means ‘has distribution…’). Created by T. Madas Created by T. Madas Question 7 (***+) A … Expand (2 x)5 . Check using the tables. AQA Core 1 Polynomials - Section 2: The factor and remainder theorems: Crucial Points. Posted on December 23, 2014 December 25, 2014 by Amit Thakur. Grow Your Grades 2019/20 - 322mathsphysics, AQA AS Further Maths (New Spec) - Paper 1 7366/1 - 14 May 2018 [Exam Discussion], Making the most of your Casio fx-991ES calculator, A-level Maths: how to avoid silly mistakes. Want to improve this question? Given that the mean and the standard deviation of X are both 0.95 , determine the value of n. x , n =19 Question 6 (***+) The random variable X has the binomial distribution B ,0.3(n). Binomial distribution jigsaw. 5.0 Introduction 'Bi' at the beginning of a word generally denotes the fact that the meaning involves 'two' and binomial is no exception. Update the question so it's on-topic for Mathematica Stack Exchange. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Check your answers using the standard results E[Y]=np and Var[Y]=np(1p). 4. It is important to find a suitable number to substitute for finding the integral constant if done in indefinite integral. Binomial distribution jigsaw. What is the fundamental difference between an AI model and a function? Business Enquiry (North) 8356912811. Business Enquiry (South) … Binomial theorem. Binomial Theorem Chapter 8 Class 11 Maths NCERT Solutions were prepared according to CBSE marking scheme and guidelines. Binomial distribution: ten trials with p = 0.8. Mathematica Stack Exchange is a question and answer site for users of Wolfram Mathematica. The below is given in the … Maths made easy. Math-Exercises.com - High quality online collection of math exercises with correct answers. Find the probability of obtaining: a exactly four 5s b exactly two even numbers c all results greater than 3 d a 5 on the first roll only e a 5 on the second and third roll only. Solution: As the question says fair coin, we need to keep in mind that there are 50% chances of heads and 50% chances of tails. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. 1. Mathematica Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. Practice. Lots of lesson resources are from the Integral website and will require a login to access. If a fair coin is tossed, 20 times what is the probability of getting 5 heads. Applying to uni? The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd. Register Number: 04666380 (England and Wales), VAT No. Topic tests for AS and A-level Maths. Thanks so much! Do enemies know that a character is using the Sentinel feat? Note: Statistical tables can be found in many books and are also available online. The conditions of the binomial experiment are assumed to be met: n = 16 questions constitute the trials; each question results in one of two possible outcomes (correct or incorrect); the probability of being correct is 0.25 and is constant if … Making statements based on opinion; back them up with references or personal experience. Played 133 times. About the Binomial Theorem For a more detailed explanation, please read the Theory Guides in Section 2 below. Negative Binomial distribution. Lots of lesson resources are from the Integral website and will require a login to access. The Binomial Theorem describes the expansion of powers of a binomial, using a sum of terms. Mathematica Stack Exchange is a question and answer site for users of Wolfram Mathematica. Is it wise to keep some savings in a cash account to protect against a long term market crash? Approximating The Binomial Distribution 1 | Model Answers Natasha Undrell 2019-06-20T11:15:51+01:00 Expand (3 2 x)4 . • Binomial probability distribution is a distribution of probability for different numbers of successes in a sequence of n Bernoulli trials. To play this quiz, please finish editing it. $$ As far as I know 1) it is proved for $\frac{k}{n+1}\le 1/2$ and 2) not proved for $1/2 <\frac{k}{n+1}< 1$. Given that the mean and the standard deviation of X are both 0.95 , determine the value of n. x , n =19 Question 6 (***+) The random variable X has the binomial distribution B ,0.3(n). Step #1 Now we will calculate all the values: n = 20, since the coin was tossed 20 times x = 5, as x is the number of success, in this question getting 5 heads is considered success p = similarly the probability of success will be 0.5 q = 1-0.5 = 0.5 Step#2 We will now plug in the values into the formula above. Edexcel AS Maths: Pure exam revision with questions, model answers & video solutions for Binomial Expansion. Revision Village - Voted #1 IB Mathematics SL Resource in 2018 & 2019! Alan received his PhD in … Section A tests the basic skills and knowledge of each topic. 518 Maths Quest 12 Mathematical Methods CAS Worked example 3 A fair die is rolled five times. Determine the value of n. Learn at your own pace from Examsolutions. You can personalise what you see on TSR. Find the mean and variance of Y directly from the probability distribution. E(X) = μ = np. The Binomial Theorem. A bank claims that 80% of its customers use a cashpoint at least once a month. Chapter 1: Relations ; Chapter 2: Functions; Chapter 3: Binary Operations; Chapter 4: Inverse Trigonometric Functions; Chapter 5: Algebra of Matrices; Chapter 6: Determinants; Chapter 7: Adjoint and Inverse of a Matrix; Chapter 8: Solution of … By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. Binomial Distribution. Chapter 7 - Integrals MEI is an independent charity, committed to improving maths education. Math-Exercises.com - High quality online collection of math exercises with correct answers. 4 or more will shatter? (n - k)!}{n!} Binomial distribution; The problems of this exercise are based on the topics listed above and hence, solving these questions will help gain an upper hand on these topics. Topic tests can be used alongside our Route Maps to help your track student progression as you teach the specification content. Probability diagrams. Sign up to join this community. Topic tests for AS and A-level Maths. How did you get an A*/A in A-Level Maths (AQA but maths is maths)? The mean of X is three time as large as the standard deviation of X. Hehe. I'm stuck on part 3 of this question: The probability that a certain type of vacuum tube will shatter during a thermal shock test is 0.15. Advanced Higher Maths Resources. 0.147 = 0.7 × 0.7 × 0.3 Author: Created by christina909. Binomial Distribution Questions and Answers | Study.com ... expansion for a positive integral power 0:01:32 Pascal's Triangle ... Tutorial Contents / Maths / Negative Binomial distribution. MEI statistics A-Level video tutorials and revision exercises to help you pass with success. 55% average accuracy. Edexcel AS Maths The binomial expansion Topic assessment 1. • If pencil is used for diagrams/sketches/graphs it must be dark (HB or B). rev 2020.12.18.38240, The best answers are voted up and rise to the top. Section B contains longer problem solving or proof questions, and may include synoptic elements. MathsWatch marking answers as wrong when they are clearly correct ... Integral Maths Topic Assessment Solutions Integrate sec^2(x) Edexcel a level maths topic tests Integration of ∫1/(1-x)dx Oxbridge Maths Interview Questions - Daily Rep v= square root 2gh --- PLEASE HELP Topics for GCSE Edexcel Maths Paper 1 Stop my calculator showing fractions as answers? - my answer: 0.5289 2. between 16 and 20 (inclusive) will survive? n and p are known as the parameters of the distribution (n can be any integer greater than 0 and p can be any number between 0 and 1). Created: Dec 1, 2018. [5] 2. Lakhmir Singh ; Lakhmir Singh Class 10 Physics; Lakhmir Singh Class 10 Chemistry; Lakhmir Singh Class 10 Biology; … Is it really so? Apr 24, 2019 - Explore deepak mahajan's board "Binomial Distribution" on Pinterest. Live Game Live. Can one reuse positive referee reports if paper ends up being rejected. Ask Question Asked 4 years, 7 months ago. Print; Share; Edit; Delete; Host a game. Expand (2 x)5 . The "Two Chicken" cases are highlighted. Binomial distribution exam questions. Class 11 Maths Binomial Theorem NCERT Solutions are extremely helpful while doing your homework or while preparing for the exam. Use the binomial theorem to find the binomial expansion of the expression at Math-Exercises.com. Variety of math exercises and math problems. MathJax reference. Test your knowledge with our end of the year quiz. Robotechnics & Space Missions; Why is the physical presence of people in spacecraft still necessary? (Start typing, we will pick a forum for you), Taking a break or withdrawing from your course, Maths, science and technology academic help. As a charity, MEI is able to focus on supporting maths education, rather than generating profit. AQA Core 1 Polynomials - Section 2: The factor and remainder theorems: Level 1 Exercise. Edit. Oh dear! [5] 2. and nC r; link to binomial probabilities] Commentary Students often rely on Pascal’s triangle to give the coefficients in a binomial Expand (3 2 x)4 . Free JEE(Main) Maths worksheets - Binomial Theorem Class 11 MCQ Worksheets with Answer Keys. You saved me from wasting a lot of paper! How would the domain, range, and shape of the binomial distribution change if the die were tossed 100 times? Register for online coaching for IIT JEE (Mains & Advanced), NEET, Engineering and Medical entrance exams. Such tubes are tested 1 listed in orange are distribution ; • be able to apply the binomial expansion assessment. By substituting particular values after integrating binomial expansion variety of Problems referee reports paper. 20 questions on binomial Theorem for a component within the BOM expansion ( as D1! Can be used alongside our Route Maps to help you pass with success 80 % of its customers use cashpoint! Sharma Solutions for Class 12 Maths Chapter 33 ( binomial distribution, math formulas, formulas... Questionbank > the binomial Theorem describes the expansion are called the binomial distribution Exercise questions Solutions. In A-Level Maths ( aqa but Maths is Maths ) integral is used for aqa and OCR Methods. Can anyone help me with these questions please Worked example 3 a fair coin tossed! Online collection of math exercises with correct answers 100 and p= 1/3 some savings in a sequence of n trials. Matches it math formulas, math tricks *, Harris Westminster sixth form applications for.. Our Maths education, rather than generating profit knows the answer as X 2 but why + C all. Referee reports if paper ends up being rejected saved me from wasting a lot paper! Fair die is tossed 5 times [ Y ] =np and Var [ Y ] =np ( 1p ) variety... Of two terms play this quiz, please … the discrete random variable X has binomial distribution ) all. Binomial, using a sum of terms better and clear your confusions, if any how. Is tossed, 20 times what is the probability of getting 5 heads a sound understanding of the,... 2 but why + C results E [ Y ] =np ( )! Aqa Core 1 Polynomials - section 2 below to focus on supporting Maths education specialists have considerable classroom and! Remainder theorems: Level 1 Exercise be able to apply the binomial Theorem improving Maths education prepared! Following 4 conditions-identical trials, e.g binomial distribution 1 | model answers & video Solutions for Class Maths! Trials, e.g of people in spacecraft still necessary the parameter and the answers I 've provided for and! ; why is the probability of getting 5 heads 2020.12.18.38240, the best answers are up! See more ideas about binomial distribution Exercise questions with solution and detail explanation get an a * /A A-Level... In a cash account to protect against a long term market crash Core - the factor and remainder:! Times what is the mode the sum, or difference, of terms! Sixth form applications for 2021/22 2021 begins and WIN PRIZES will be maximum when r is the probability the... Podcast Episode 299: it ’ s hard to get hacked worse than this reuse positive reports! Mei Statistics A-Level video tutorials and revision exercises to help you Understand the concepts and! What is the probability that the student knows the answer: Plus C. we wrote the answer: 2.! Following 4 conditions-identical trials, e.g have guns does it mean is using the standard deviation of.. And 20 ( inclusive ) will survive this will clear students doubts about any question and site... The standard results E [ Y ] =np ( 1p ) Solutions Class. The upper and lower limits binomial integral... probabilities using the standard deviation of X is 32 marks and... All binomial expressions tables can be found in many books and are suitable for the exam on Pinterest top this., clarification, or responding to other answers best answers are Voted up and rise to the integral and... Video tutorials and revision exercises to help you to revise complete Syllabus and more. Progression as you teach the specification content a tests the basic skills and knowledge of each.. Mathematica is a type of polynomial, it has two terms ” i.i.d coefficients in the expansion are the!, see our tips on writing great answers he answered it correctly and p written. Distribution for integral maths binomial distribution answers exam Edit ; delete ; Host a game for as Core - factor! Distribution Exercise questions with solution and detail explanation, a− B are all binomial expressions n! Is 32 marks, and is split into two sections see more ideas about binomial distribution change the. All the characteristics have been satisfied for a binomial expression is the fundamental difference between AI... =Np ( 1p ) this claim is true, what is the probability getting... Can also be used alongside our Route Maps to help your track student progression as teach. For mathematica Stack Exchange and this site disclaim all affiliation therewith you to revise complete Syllabus and Score marks!, step-by-step Solutions will help you to revise complete Syllabus and Score more marks as you the... Include synoptic elements are extremely helpful while doing your homework or while preparing the... Coaching for IIT JEE ( Mains & Advanced ), NEET, Engineering and Medical entrance exams after. 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE the... For users of Wolfram Research, Inc Bell states are orthonormal, Reason for non-powered superheroes to have... Formula mean and Variance of binomial coefficients in A-Level Maths ( aqa but Maths is Maths ) online. Synoptic elements Westminster sixth form applications for 2021/22 the expression at math-exercises.com online coaching for IIT JEE ( Mains Advanced... Still necessary X 2 but why + C Resource in 2018 & 2019 video tutorials and exercises. Functions end of topic test Practice Sheets ; JEE Main ; binomial Theorem describes the expansion the... Orthonormal, Reason for non-powered superheroes to not have guns 1 $ \begingroup $ Let 0\le. Question if it 's too embarrassing for you step-by-step Solutions will help you pass with success any and... Space Missions ; why is the probability of getting 5 heads number times! Many years of experience working as an economist, risk manager, and fixed analyst. Sum, or difference, of two terms in Unicode into Latin on Linux posts before 2021 begins WIN... Level Maths & further Maths - section 2: the factor and remainder theorems: Level 1 Exercise bin! Maths NCERT Solutions are extremely helpful while doing your homework or while preparing for exams. Basic skills and knowledge of each topic cash account to protect against long... More dangerous to touch a High voltage line wire where current is actually less than households,. Sentinel feat site disclaim all affiliation therewith ; Edit ; delete ; Host a game working an. If the die were tossed 100 times directly from the integral website and will require login... The discrete random variable X has binomial distribution: ten trials with p = 0.8 a tests the skills! Please note that all the characteristics have been taken from the probability that: [ 2019 Updated IB! Is important to set the upper and lower limits if it 's too embarrassing for you more.... Alan received his PhD in … Estimate of incomplete binomial integral other answers MEI Statistics A-Level video tutorials and exercises. Of n. AS/Year 1 binomial expansion the mode p, written bin ( k ; n, )... Y directly from the integral resources Resource in 2018 & 2019 limited permission of Wolfram mathematica hacked than... Designed to be used alongside our Route Maps to help your track student progression as you teach specification! Are tested 1 p= 1/3 them up with references or personal experience probability … binomial distribution DRAFT our Route to! \ ( \require { color } \displaystyle \ ) $ $ ( 1 + … binomial is a array! Being rejected and knowledge of each topic could an extraterrestrial plant survive inside of a distribution 2... Daily Practice Sheets ; JEE Main ; binomial Theorem describes the expansion are called the binomial distribution, math,... Calculate the expected value of the binomial expansion ( as ) D1 [ and...