Binomial Definition and 640 Threads

Hey, I'm new to all this so cut me some slack, but have been trying to work through some questions, and I can't seem to find answers to these questions... Or atleast find the confidence that my answers/working is correct... 1. (Exponential Distribution) Telephone calls arrive at the...

Homework Statement Gerry Infield has batting average of 0.326 what is the probability that he will have two hits in his next 5 times at bat?Give your answer correct to 3 decimal places. The Attempt at a Solution It is a binomial distribution with n trails and x sucesses (hence, n-x...

Homework Statement My book says that one "easily" verifies that (x+y)^n = (x + y)^(n-2)Q+(x+y)^(n-3)P where Q = x^2 + xy +y^2 and P = xy^2 + x^2y Homework Equations The Attempt at a Solution I began by expanding everything into summations with binomial...

Homework Statement Find the radius of converge of: \sum[SIZE="4"]x^{}(n choose k) Homework Equations Radius of converge = 1/limsup|an+1/an|, for power series: anx^n The Attempt at a Solution Tried rewriting (n choose k) as: n!/[k!(n-k)!] but where do I...

Ok so I have a problem I am not sure of the method I should use. In a recent survey, 60% of the population disagreed with a given statement, 20% agreed and 20% were unsure. Find the probability of having at least 5 person who agree in a mini-survey with 10 people. I tried to caculate the...

Prove the following statement: \[ \sum\limits_{r + s = t} {\left( { - 1} \right)^r \left( \begin{array}{c} n + r - 1 \\ r \\ \end{array} \right)} \left( \begin{array}{c} m \\ s \\ \end{array} \right) = \left( \begin{array}{c} m - n \\ t \\ \end{array} \right) \] Any initial...

Use binomial theorem to prove C(n,0) - 3(C(n,1)) + 9(C(n,2) - 27(C(n,3) + ... + (-3)^n(C(n,n) = (-2)^n From looking at the data given b = (-3) so a = 1 so (-2)^n = (1-3)^n With this I know the equation in sigma notation and could probably prove the theorem through mathematical induction but...

I learned the Binomial Theorem a while ago. But it is only now that I think about how it is only useful for powers that are natural numbers. Can it be extended to all real numbers - e.g. 1/2?

Homework Statement I'm having a lot of trouble solving for part b as I am unable to correctly apply the binomial theorem to this approximation. The problem is shown below: Three point charges are distributed: a positive charge +2Q in the center, and a pair of negative charges -Q, a...

Hi. I'm completely stuck on the following question, and have no idea how to even start it. Any help would be really appreciated. The first four terms, in ascending powers of x, of the binomial expansion of (1 + kx)^n are 1 + Ax + Bx^2 + Bx^3 + ..., where k is a positive constant...

Homework Statement Show that if n is a positive integer, then 1\,=\,\binom{n}{0}\,<\,\binom{n}{1}\,<\,\cdots\,<\,\binom{n}{\lfloor\frac{n}{2}\rfloor}\,=\,\binom{n}{\lceil\frac{n}{2}\rceil}\,>\,\cdots\,>\binom{n}{n\,-\,1}\,>\,\,\binom{n}{n}\,=\,1 Homework Equations I think this proof involves...

Hi, Im having some troubles with this binomial expansion... Determine the coefficient of x^k, where k is any integer, in the expansion of (2x - 1/x)^2007. I figured it would just be C(2007,k) * (2x)^2007-k * (-1/x)^k = C(2007,k) * (2)^2007-k * x^2007-k * (-1/x)^k therefore the...

Homework Statement Sum the following series to N terms: C_0^2-2C_1^2+...+(-1)^n(n+1)C_n^2 Arrgh! This is a very frustrating question. I have to multiply two series and find the coefficient of some term but I don't know what to do. Please don't ask me to give you some proof of my work at...

I'm really confused when it comes to this stuff. I'm stuck on this problem: (2c - 3d)^5 I have no idea where to begin. Please help!

Homework Statement Expand (1-6x)^4 (1+2x)^7 in ascending powers of x up to and including the terms in x^3 Homework Equations (1-6x)^4 (1+2x)^7 The Attempt at a Solution Firstly, I expand (1-6x)^4 = (1)^4 + 4C1 (-6x) + 4C2 (-6x)^2 + 4C3 (-6x)^3 + ...

Ok i need help to calculate the co-efficients of certain terms in the binomial expansion for example: (3 + (5/X)^2)^10 what is the coefficient of x^8? I hope that question works sorry if it doesn't i did just make it up then... if you know of any like it please help! also, an...

Hi, Can anyone explain binomial distribution to me. I tried wikipedia and some googling, but I just do not understand much of it. I don't come from maths background, I am more like an IT person. I need to write a short program calculating binomial distributions, however, first I need to...

I was reading through a proof of the summation formula for a sequence of consecutive squares (12 22 + 32 + ... + n2), and the beginning of the proof states that we should take the formula: (k+1)3 = k3 + 3k2 + 3k + 1 And take "k = 1,2,3,...,n-1, n" to get n formulas which can then be...

Hello everyone. I'm studying for my exam and I'm reveiwing some problems but this one isn't making sense to me: 11^9(9 choose 0) - 11^8(9 choose 1) + 11^7(9 choose 2) - ... - 11^2(9 choose 7) + 11^1 (9 choose 8) - 11^0 (9 choose 9) answer: (11-1)^9 = 10^9 = 1,000,000,000. work...

Binomial Expansion Question Driving Me Mad! http://img489.imageshack.us/img489/5239/binomialiv6.jpg This is the last question on my maths sheet, and i must have been staring at it for hours, I've read all my notes and book but i just can't piece it together at all. Driving me crazy...

Is it always necessary that C(n,r) is an integer if n and r are integers ? Is there any proof ?Please clarify. thanks.

How do I do this p(x<1) this sign has a _ under the < n=6 p=0.1 Suppose x is a discrete, binomial random variable. Calculate P(x > 2), given trails n = 8, success probability p = 0.3 [Hint: P(x > value) = 1 – P(x <= value) <= is a < with a _ under it (tell me the number...

There are a few questions that have been giving me trouble with this binomial theorem stuff. (1). Using the binomial theorem and the relation (1+x)^{m_1} (1+x)^{m_2} = (1+x)^{m_1 + m_2} prove that: \sum_{k=0}^n \binom{m_1}{k} \binom{m_2}{n-k} = \binom{m_1 + m_2}{n} (2). Prove by induction...

How does one deduce the following: We are given \binom{-3}{n} = \frac{(-3)(-4)(-5)\cdot\cdot\cdot\cdot\cdot(-3-n+1)}{n!} = \frac{(-3)(-4)(-5)\cdot\cdot\cdot\cdot[-(n+2)]}{n!} . How do we get from here to: \frac{(-1)^{n}\cdot2\cdot3\cdot4\cdot5\cdot\cdot\cdot\cdot(n+1)(n+2)}{2\cdot n!} =...

Here is the question from the book: By integrating the binomial expansion, prove that, for a positive integer n, \frac{2^{n+1} - 1}{n+1} = 1 + \frac{1}{2}\binom{n}{1} + \frac{1}{3}\binom{n}{2} + ... + \frac{1}{n+1}\binom{n}{n} ------------ So I integrated both sides of the following...

f_r=(\frac{1+v}{1-v})f_i For an automobile moving at speed v that is a small fraction of the speed of light, assume that the fractional change in frequency of reflected radar is small. Under this assumption, use the first two terms of the bionomial expansion (1-x)^n\approx{1-nz \mbox{for}...

How would you quickly derive the binomial series? Would you have to use Taylor's Theorem/ Taylor Series? And does the Binomial Theorem follow from the binomial series? Are there any applications at all of the binomial series/ Binomial Theorem to special relativity? I know the binomial series is...

Hi all, I am working on the last part of a problem now in which I am trying to find what velocity (as a fraction of c) must be traveled from the Earth to Andromeda (a distance of 2.00x10^6 light-years) in order for only 20 years to pass in the reference frame of the rocket. I created my...

I am trying to prove (or find a counterexample for) this: Let n be any positive integer, and m any odd integer, with 1 <= m < 2^n. Also, let B(x,y) denote the binomial coefficient, x! /( y! ( x - y )! ). Then 2^n | B( 2^n , m ). Any help is welcome.

1. For each of the following, simplify so that the variable term is raised is to a single power: (a) State the General Term tr in the Binomial expansion of (2x^2 - 1/x)^10 (b) Find the 7th term in the expansion (c) Is there an x^5 term? Find its coefficient. (d) Is there a constant term...

i an havign trouble solving this qs if nC0 + nC1 + nC2 +...+ nCn = 256 find the value of n all help appreciated:smile:

A question: Let bin(a,b) denote the binomial coefficient a! / ( b! (a - b)! ). Is it true that bin( 2p, p ) = 2 (mod p) if p is prime and p>=3 ?

Suppose you have n elements with integer keys and they are to be put into a heap. What would be the time for creating a heap by repeated insertion into into an initially empty heap? Say, for instance if we are using binary, binomial and fibonacci heap type. Any suggestions?

Dear Fellow mathematicians and Physicists,I am doing some MC modelling on tumour growth and radiotherapy treatment modelling and would like to know: Who out there would agree (or suggest alternatives) to the theroy that the chance of a cell being damaged/hit with radiation (and therefore...

Hi I wanted to know what is the expansion of (1+x)^n when n is a rational number and |x|<1 ... Please let me know as soon as possible.. Thanks for your help Sincerely Sparsh

Is there a way to derive P (X=r) =^nC_r p^r q^{n-r} , r= 0, 1, 2,..., n where X: B(n,p) where n is the total number of bernoulli experiments, p the probability of success q, the probability of failure.

There was a question on the test with the following information (binomial distribution) n=10 p=.2 Find the probability that X is : a. At least 3 b. At most 3 For part a I did P(X>=3)=1-P(X<=2) For part b I did P(X<=3) : \sum_{x=0}^3 perm(n, x)*p^x*(1-p)^(n-x) The last part is...

Okay so I did this problem and got it wrong but I get one more chance to get it right. I tried using Binomial Dist to solve it but I failed. 30% of all M&Ms are brown. If 7 M&Ms are randomly selected, what is the probability that at most 1 is brown? I thought I would use 0 and 1 but I...

I'm a complete beginner at these: (3n+1)^3 = (3n)^3 + 3(3n)^2 + 3(3n)^2 + 1 which would give me = 3 (9n^3 + 6n^2) +1 is this correct?

Could anyone tell me what (3n + 2)^x equals to please so I can check my answer? I get something awful that would take me too long to type

I'm having problems figuring out how to do part (b) of this question. a) expand (1-2x)^3 and (1+1/x)^5 b) Find, in the expansion of (1-2x)^3 (1+1/x)^5 i) the constant term ii) the coeffecient of x I've done part a, and I know the formula for a general term for an expansion of a...

Hi! Does someone know how to solve this equation (see the link) if all variables are known without P_U (without using a computer program)? http://www.itl.nist.gov/div898/handbook/prc/section2/gifs/pueq.gif Can it be done in some easy way? I have read courses in calculus at the...

By writing (1+x) as \frac{1}{2}\left[1+\left( 1+2x\right) \right] or otherwise, show that the coefficient of x^n in the expansion of \frac{\left(1+x\right)^n}{\left(1+2x\right)^2} in ascending powers of x is \left(-1\right)^n\left(2n+1\right). -- I've tried expressing (1+x)^n as...

So the problem gives a binomial random variable X with parameters n=5 and p=0.25 and ask for the probability P(X=1.5). The binomial probability mass function is defined only for integers. Should i approximate using the normal distribution or the poisson?

anyone could help me with this question... in the expansion of (ax + by)^n, the coeffiients of the first 3 are 6561, 34992, and 81648., Find the value if a, b, and n. i did this... t1 = nC0 (ax)^n = 6561x^n a^n = 6561 t2 = nC1 (ax)^n-1 (by)^1 = 34992x^n-1y bna^n = 34992 but I'm not...

Hello I'm suppose to show Given z^4 + z^3 + z^2 + z + 1 = 0 where z = cos(\frac{2 \pi}{5}) + i sin(\frac{2 \pi}{5}) by using the binomial product formula. r^n - s^n Is that then if r,s = z then z^4 - z^4 = 0 ? Sincerely and Best Regards Bob

Show that if x is small then 1/(1+x) - root(1-2x) ~= (3/2)x^2 im not sure how to even begin this question. there was a part 1 but i don't think its relevant. Small numbers just confuse me...how small is small in any case?

Hello, another dull question on binomial expansion (approximation). I cannot follow the derivation for the approximate values of the two constants \alpha and \beta. (Text on propagation coefficient of TEM waves in transmission lines - constants of attenuation and phase-shift) Given \gamma...

I understand how Binomial expansion works, but I don't understand how to solve this problem. Give the term of (2/x^2-x)^6 that has no x.

"Show that for small values of x, the function (1+x)^(-1/2) may be approximated by 1-(1/2)x+(3/8)x^2 Hence obtain the approximate value of 1/root(1.01) to 4 decimals." im totally clueless. the example we have isn't well explained at all. can someone even just start me off...