Binomial Definition and 640 Threads

Homework Statement For a certain species of bird, there is a chance of three in five that a fledgling will survive. From a brood of ten chicks, find the chance that more than one will survive. Let p = survival chance = 3/5 Let q = non-survival chance = 2/5 P(less than one will not...

How do I find a conditional bionomial distribution? For example, if I want the probability that k=7 (for instance, 7 could be any number depending on the experiment), given that k is greater/equal to 4. I know what the equation would look like i.e.: F(k=7|k >= 4)= P(k=7, k>=4)/P(k>=4)...

How can I find probability p that maximized P(Y = y*) when Y has a negative binomial distribution with parameters r (known) and p? I've just reduced the problem with some algebra, but other than guess-and-check I have no rigorous way to solve this problem.

Homework Statement Ok, I know that (-1)^r \binom {n} {r} is supposed to equal 0. But I have plugged some numbers into this series, and this doesn't seem to be true for even numbers of n? Like for n = 4 and r = 4, I have: 1 - \frac{4!}{1!3!} + \frac{4!}{2!2!} - \frac{4!}{3!1!} +...

Hi all, this homework problem's been driving me nuts. It seems like it's probably pretty straightforward and I'm missing something obvious, but I just can't work it out. Homework Statement prove that if p is a prime number that p|B(p,m) where B(p,m) is the ordinary binomial coefficient...

I havn't done this in a long time! And apparently I should know this easy, it sort of looks like a proof by induction, which I havn't done before and I am frantically trying to learn! Show that for each integer n the alternating sum of binomial coefficients: 1 - (n) + ... + (-1)^k(n) + ...

Homework Statement To Prove: (nC0)(mC0) + (nC1)(mC1) + ... + (nCm)(mCm) = (n+m C m) where nC0 = n choose 0 and so on. Homework Equations The Attempt at a Solution Tried expanding the whole thing using factorials - but didn't work. Any hints would be really welcome!

How to Find the Probability of rolling at least 2 "sixes" in 6 rolls of a balanced die. I am trying to solve using the Binominal Formula, P(X = r) = nCr p r (1-p)n-r But am not really sure what the probability rates for success and failure should be or how to compute it. Any advice? Thanks.

Homework Statement Homework Equations What is the integral of \int^{0}_{1} nCy x^{y} (1-x)^{n-y} dx ? The Attempt at a Solution \left(nCy\right) \int^{0}_{1} x^{y} (1-x)^{n-y} dx

How would you expand (x+y)^0.5 ?

Homework Statement Well, I was trying to expand say for the third power of (A+B), where A and B are non-commutative. The Attempt at a Solution I get (A+B)^3=(A^2+AB+BA+B^2)(A+B)=A^3+ABA+BA^2+B^2A+A^2B+AB^2+BAB+B^3 but from a few sources online, it should be...

hello, i need to prive that for a binomial r.v X E[X]=NP and VAR(X)=NP(1-P). I tried to prove it using the deffinition of expectation: E[x]=\sum xi \stackrel{N}{i} p^{i}(1-p)^{n-i} now what? thanks...

Homework Statement A game is played by tossing two unbiased coins repeatedly until two heads are obtained in the same throw. The random variable X denotes the number of throws required. Find the expression for P(X=r). Homework Equations The Attempt at a Solution It looks to be a...

Here's the actual problem I'm faced with. Suppose a segment of dna with 100 mutations (SNPs) which occur at different frequencies from each other and between 2 different populations for the same mutation. The expected number of mutations occurring in the segment of dna is different in either...

Homework Statement Find, in the simplest form, the coefficient of x^n in the binomial expansion of (1-x)^(-6). Homework Equations The Attempt at a Solution i am not sure how to go about with this.

In my book, it says that the Binomial Series is \sum_{n=0}^{\infty }\binom{n}{r} x^n Where \binom{n}{r} = \frac{n(n-1)...(n-r+1)}{n!} for r\geq1 and \binom{n}{0} = 1 Now here is where it got to be, I know that the \binom{n}{r} = \frac{n(n-1)...(n-r+1)}{n!} were derived through the...

sum_{i=k}^{n} {i \choose k}i^{-t} where t is a constant. Does it have a closed form?

How is 1+p+\frac{p^2}{2!}+\frac{p^3}{3!}+...=e^p ?

Hello everyone, Just have a quick question on a binomial problem. The problem is as follows: A teacher is giving a 15 question true-false quiz. He wants to design the quiz such that a person that guesses on all the answers have less than a 0.10 probability of passing. What should the...

Homework Statement Given a series of 0 and 1 , how can we plot the binomial curve ?? Example: 00000011100010010100011110 say,p=0.8 q=0.2, N=26 Homework Equations If I apply the classic binomial formula, 26C0 (0.8)^0(0.2)^(26-0) etc.. seems cannot do so.

Homework Statement This is the given Theorem in my book, everything seems fine except that I cannot figure how they expanded (xn - an) Homework Equations The Binomial Theorem The Attempt at a Solution According to me (xn - an) = {[(x+a)-a]n - an} and expanding it would yield...

Homework Statement (here, (n,k) reads n choose k) prove that (n,0) - (n, 1) + ... + (-1)n(n,n) = 0 Homework Equations binomial theorem The Attempt at a Solution so this proof is relatively straightforward when n is odd. it's just matching up terms and having them cancel each other...

Dear Friends, I want to find an upper and lower bound for the expected value of the minimum of independent binomial random variables. What paper/book do you suggest for this problem? In other words, I need to find bounds for E(min(X1,X2,...,Xn)), where Xi 's are independent random variables...

I am trying to follow along with this derivation of the binomial distribution formula: b(x;n,p) = nCx*pxqn-x But I do not really understand the meaning of the part on bold. What is this "specified order" business now? I feel like I am missing something big here.

i was told the binomial theorem is as follows: (1-x)^n = 1-nx+ (n(n-1)/2!)x^2 - (n(n-2)/2!)x^3 ... not sure if this is right could some one clear this doubt for me any help is appreciated was told this in a physics class

Homework Statement How can i prove this relationship \sum _{i=0}^k \text{Binomial}[n+1,k-2i] - \sum _{i=0}^k \text{Binomial}[n,k-2i]=\sum _{i=0}^k \text{Binomial}[n,k-1-2i] Homework Equations Binomial (n,k)=n^k/k! The Attempt at a Solution I attempted subbing into mathyematica but this didn't...

by using binomial distribution if two coin are tossed 4 times ,find? 1)the probability of 2 heads in 4 times ? 2)the probability of less than one head once? 3)the probability of than 2 tails in 3 times ? 4)the expected number of two tails ? 5)the variance of the number of 2 heads?

Homework Statement My question is simple is there a formula for the bi/tri-nomial expansion of bi/tri-nomials raised to fractional powers. that is, (x^{2}+1)^{1/2} or (x^{2}+x+1)^{1/2} I know pascals triangle for integer exponents but i can't really find anything about fraction...

Homework Statement (n¦0)-(n¦1)+(n¦2)-. . . ± (n¦n)=0 that reads n choose zero and so on Homework Equations Prove this using the binomial theorem The Attempt at a Solution I really have no idea where to start. Any help would be greatly appreciated thanks

I understand permutations, combinations and such, but I can't seem to make sense of binomial coefficients, or at least the notation. As an example, could someone walk me through the notation for a generic problem.. something like 100 people eligible for an award and the winner can choose 1...

If we have numbers 1,2,3,4,5,6,7,8,9,10,11. We want to pick 5 numbers out of that, but there is a restriction - the summation of the 5 picked numbers must be 21 or less. How many different combinations can we get? The answer is 24 but I would like to know how to work it out (besides...

Homework Statement Find the minor value of the natural number n such that \left (\frac{\sqrt{3}}{2} + \frac{1}{2}i \right )^{n} be a real positive number. EDIT: n must not be 0. Homework Equations Considering the binomial theorem as: {\left(x+y\right)}^n=\sum_{k=0}^n{n \choose...

From the central limit theorem the binomial distribution can be approximated by a normal distribution N(0,1). But the binomial distribution can also be approximated by a poisson distribition. Does this mean there is a relationship between the normal distribution and the poisson distribution...

One of the questions in my probability homework reads: X denotes a negative binomial random variable, with p = 0.6 Find P(X ≥ 3) for a) r = 2 and b) r = 4. According to my teacher, the answers are 0.1792 and 0.45568, respectively, but I can't for the life of me figure out how he got them...

Hi, I'm using a website (http://stattrek.com/Tables/Binomial.aspx) to calculate binomial probability, and I cannot understand it's output. Consider: 1.13860032513458E-11 Does this mean 1.13860032513458^[e*(-11)] Thanks

Homework Statement Show that: (\stackrel{n}{k})=\#\left\{(\omega_{1},..., \omega_{n})\in\left\{0,1\right\}^{n}:\Sigma^{n}_{l=1}\omega_{l}=k\right\} (edit: the sigma is meant to go from l=1 to n) Homework Equations It says to use this...

Homework Statement Calculate \sqrt{1/20} using the extended binomial theormem. (a precision of k=4 is enough) The Attempt at a Solution \sqrt{1/20}= (1 + (-19/20) )^{1/2}= \sum( choose (1/2,k)*(-19/20)^k) = 1- 1/2*19/20-1/8*361/400+1/16*6589/8000 = 0.72... is wrong. Homework...

Homework Statement Express cos^4Θ.sinΘ in the form asinΘ+bsin3Θ+csin5Θ Homework Equations cosrΘ = 1/2(z^r + z^-r) sinrΘ = 1/2i(z^r - z^-r) The Attempt at a Solution So far I think I have this. 32i(sinΘ)(cos^4Θ) = (z-z^-1)(z+z^-1)^4 I am unsure how to multiply and manipulate...

Homework Statement Find the term in the expansion of (x-(2/x^2))^14 which is of the form constant/x. The Attempt at a Solution I have worked out the general expression. (14|r) x^14-r * (-2/x^2)^r However I can only work out this problem by trial and error. I know that in this case...

Homework Statement Show that for all integers n,m where 0 ≤ m ≤ n The sum from k=m to n of {(nCk)*(kCm)} = (nCm)*2^(n-m) The Attempt at a Solution So for the proof, I have to use a real example, such as choosing committees, binary sequences, giving fruit to kids, etc. I have been...

Homework Statement (Give a combinatorial proof of each of the following identities. In other words, describe a collection of combinatorial objects and then explain two different methods for counting those objects. Leave each identity in the form given. Do not rearrange terms or use any other...

can anyone help with this:

Homework Statement For fixed n, are there values of p (0≤p≤1) for which V(X) = 0? Explain why this is so. The Attempt at a Solution For X~Bin(n,p), V(X)=np(1-p). So the only solutions for this equation are when p=0 or p=1. There are too many variables for me to keep track of and...

Homework Statement The College Board reports that 2% of the 2 million high school students who take the SAT each year receive special accommodations because of documented disabilities. Consider a random sample of 25 students who have recently taken the test. a.) What is the probability...

Homework Statement The rejection rate of a certain journal is 45%. If the journal accepts articles at random, what is the minimum number of articles someone has to submit to have a probability of more than 0.75 of getting at least one article accepted? Homework Equations I'm almost sure...

hi there I am abit stuck here. i got a q saying : in binomial expansion of (3-2/x)^9 find the 5th term using the general term of the binomial expansion and check your answer (3-2/x)^9 used formula =N!/(n-r)!r! * A^(n-r) * b ^ r r= 4 a= 3 b= - 2/x n=9 got a answer of -489888/x^4 How do i...

Suppose n is even, prove: \sumk=0->n/2, C(n,2k)=2^(n-1)=\sumk=1->n/2, C(n,2k-1) Give a combinatorial argument to prove that: (I've figured out this one...) \sumk=1->n, C(n,k)^2=C(2n,n) For the first problem, I tried to break C(n, 2k) into C(n+1,2k)-C(n, 2k-1), but they didnt seem to work very...

I have this question and its a combination of the binomial theorem and nilpotent elements within a ring. Suppose the following, am=bn=0. Is it necessarily true that (a+b)m+n is nilpotent. For this question I did the following: \sumi=0m+n\binom{m+n}{i}am+n-ibi If i=m, then a=0...

A text file contains 1000 characters. When the file is sent by email from one machine to another, each character (independent of other characters) has probability 0.001 of being corrupted. Use a poisson random variable to estimate the probability that the file is transferred with no errors...

Homework Statement An opaque bag contains 10 green counters, and 20 red ones. One counter is drawn at random and not replaced: green scores one, red scores zero. Five counters are drawn. Find the probability of scoring 0, 1, 2, 3, 4, 5 points. Homework Equations The Attempt at...