Binomial Definition and 640 Threads

Homework Statement Where P_n(x) is the nth legendre polynomial, find f(n) such that \int_{0}^{1} P_n(x)dx = f(n) {1/2 \choose k} + g(n)Homework Equations Legendre generating function: (1 - 2xh - h^2)^{-1/2} = \sum_{n = 0}^{\infty} P_n(x)h^n The Attempt at a Solution I'm not sure if that...

Homework Statement It says: Determine the coefficient of p4q7 in the expansion of (2p-q)(p+q)10. I can find the coefficient of p4q6 in the expansion of (p+q)10 but how am I to find it for (2p-q)(p+q)10? Homework Equations Binomial expansion formula. The Attempt at a Solution...

Hi, I have tried to calculate 200C65 on my calculator but the calculator gives an error. Do u know how to do it? I also tried to calculate it through the formula with the ! but doesn't give an answer.

http://www.examsolutions.net/maths-revision/core-maths/sequences-series/binomial/formula/validity/tutorial-1.php On the above video, he states that the binomial expansion is only valid for |a| < 1 when n is not a positive integer. I understand that when n is not a positive integer the...

Homework Statement Find the value of Ʃn(18 n)(0.46)^2(0.54)^(18-n) The sum is from n = 0 to n=18 Sorry, I do not know how to format it. Homework Equations I am using the Binomial Expansion Theorem: The Attempt at a Solution Not sure where to start. P = 0.46 Q =...

IF Y~B(11, 0.3), find (|Y-5| >= 3) I got the answer(0.3170) but i don't understand the logic behind this part where i am confused. can someone explain the working(second working) where i somehow got it blindly correct? ================================== my working at first: |Y-5|...

Homework Statement Hello, I am trying to calculate the following: 15!/(1!)(14!) x (0.80)^14 x (0.2)^1 I understand the problem as I have already put the numbers together. My trouble is actually using the calculator to find the answer. When I try to find 15! = 1.307674368^12 I am confused...

Homework Statement We have an urn with 5 red and 18 blues balls and we pick 4 balls with replacement. We denote the number of red balls in the sample by Y. What is the probability that Y >=3? (Use Binomial Distribution) Homework Equations The Attempt at a Solution Okay, so we...

Homework Statement let y_1 and y_2 be iid bin(5,1/4) random variables let v=y_1+2*y_2 and u = 3*y_1 -2y_2 find f_uv (u,v) and the cov(u,v) Homework Equations f_y (y) = (5 choose y) (1/4)^y (3/4)^5-x for x=0,1,2,3,4,5 covariance=E(uv)-E(u)E(v) The Attempt at a Solution...

Homework Statement I'm trying to solve the following question: You and n other people (so n+1 people) each toss a probability-p coin, with 0<= P \ <=1. Then each person who got a head will split some arbitrary amount of prize money, K, equally. If nobody gets a head, then nobody gets the prize...

Guess what? I just got my new calculus book last week! ^^ The book opens with the definition of the real numbers by Dedekind and goes to prove properties of this numbering system such as The supremum axiom and others. At the end of the chapter are about 30 exercises without their solutions...

I immediately thought of induction, so that is what I used, but I can't seem to make any progress past a certain point.

Hi All, Homework Statement This is algebraic proof of Vandermonde's identity: I am having some problem understanding how we reached the second last step and more importantly, last steps from revious steps. src::proofwiki.org I would be grateful if someone would elaborate it clearly...

Homework Statement Homework Equations The Attempt at a Solution do you see where it says 5 over 2 = 10 and 5 over 3 = 10. How? I don't get what they're doing.

I am doing a problem where I am to determine the probability that the number of students wanting a new book is within two standard deviations of the mean. μ +- 2δ comes out with a non integer number, in which I have to use to find probability. The equation to find probability uses the factorial...

I have an assignment which is a bit different, I have to use Mathematics Handbook for Sience and Engineering to solve the problem, I can look it up in tables. But the tables for binomial functions is only up to 20, Normal Distribution to 3.4 and Poisson up to 24 in some cases. So how do I do...

Homework Statement Expressing the binomial coefficients in terms of factorials and simplifying algebraically, show that (n over r) = (n-r+1)/r (n over r-1);Homework Equations The Attempt at a Solution I honestly don't even know how to come about this problem...I really need help in this...

Homework Statement Define (n k) = n!/k!(n-k)! for k=0,1,...,n. Part (b) Show that (n k) + (n k-1) = (n+1 k) for k=1,2,...n. Part (c) Prove the binomial theorem using mathematical induction and part (b). Homework Equations The Attempt at a Solution I'm wasn't able to...

Homework Statement How do you prove that the binomial series (x+1)^p converges for |x|<1 ? Homework Equations The Attempt at a Solution (x+1)^p = Ʃx^{n}\frac{p!}{(p-n)!n!} After doing ratio test I get |x|<1 . But now I have to test end points and this is my problem: when...

Homework Statement Prove that n^n > 2^n * n! when n > 6 using the Binomial theorem. I just proved the Binomial theorem using induction which was not that difficult but in applying what I learned through it's proof I am having difficulty. Homework Equations Binomial theorem = (x+y)^n =...

Homework Statement I've uploaded a picture of the question. I need help in identifying the correct number of trials, probability of success and the X value(number of successes) Homework Equations i'm using the binomial distribution function on the calculator but I've attached the formula just...

Homework Statement Hey guys, I'm self studying some probability theory and I'm stuck with the basics. I must find the characteristic function (also the moments and the cumulants) of the binomial "variable" with parameters n and p. I checked out wikipedia's article...

Hey guys, In class, I was shown that the Binomial prob density function converges to the Poisson prob density function. But why does this show that the Binomial distribution converges in distribution to the Poisson dist. ? Convergence in distribution requires that the cumulative density...

I'm having trouble proving the following identity (I don't even know if it's true): $$\sum_{r=1}^k \binom{k}{r} \binom{n-k-1}{r-1}=\binom{n-1}{k-1}$$ $$\forall n,k \in \mathbb{N} : n>k$$ Thank you in advance for any help! Vincent

Homework Statement The probability of being dealt a full house is approximately 0.0014. Find the probability that in 1000 hands of poker you will be dealt at least 2 full houses Homework Equations I can use binomial distribution. The Attempt at a Solution The probability of getting...

Homework Statement For n trials, S_n can be seen as the sum of n independent single trials X_i, i = 1,2,...,n, with \mathbb{E}[X_i]=p and Var[X_i]=p(1-p).2. What I don't understand I don't understand why Var[X_i]=p(1-p). We know that: Var[X_i]=\mathbb{E}[(X_i - \mathbb{E}[X_i])^2] =...

Homework Statement (√2 + 1)6 = I + f Where I is the sum of integer part of the expansion of (√2 + 1)6 and f is sum of the fraction part in (√2 + 1)6. Homework Equations (x+1)n = nC0 xn + nC1 xn-1 + nC2 xn-2 + ... + nCn nCn = nC0 = 1 The Attempt at a Solution I expanded...

I have been teaching myself analysis with baby rudin. I have just started chapter three in the past week or so and one thing I am having trouble with is the proofs which use the binomial theorem and various identities derived from it. Rudin pretty much assumes this material as prerequisite and...

Homework Statement Prove the binomial theorem by induction. The attempt at a solution http://desmond.imageshack.us/Himg35/scaled.php?server=35&filename=sumu.png&res=landing Hi, running into trouble with this proof and google hasn't helped me. I don't understand the jump here, and as...

Homework Statement In each batch of manufactured articles, the proportion of defective articles is p. From each batch, a random sample of nine is taken and each of the nine articles is examined. If one article is found to be defective, the batch is rejected; otherwise, it is accepted. If...

Homework Statement What am I supposed to do with the 3 over 2 in the parentheses? It can be divide and it can be take the factorial. So what do I do with it?

Homework Statement Find the first four terms in the expansion of \left(1-3x\right)^{3/2}. By substituting in a suitable value of x, find an approximation to 97^{1/2}. Homework Equations The Attempt at a Solution I used the binomial expansion formula to work the answer and it is 1-...

I was trying to make sense of the equation attached below which was on the wikipedia site. However I'm not entirely sure how to make use of the "n choose 0" , "n choose 1", etc. statements that in front of each term in of the expansion. I roughly know how the expansion should look...

Homework Statement The method of Binomial expansion is useful because you can avoid expanding large expressions: Q: Find the term indepedent of x in the expansion of (2+x)[2x+(1/x)]5 The attempt at a solution: "For this to produce a term independent of x, the expansion of [2x+(1/x)]5 must...

how to do binomial series of (3+x)3.

Question is: "If you roll a fair coin 10 times what is the expected product of number of heads and number of tails?" Someone answered 25 at at glassdoor.com. My answer would be: E(k(10-k)) where k is the rv representing the number of heads thrown. = 10E(k) - E(k^2) = 10*mean - (var +...

I have a question about binomial distribution There is a random var X follows Binomial distribution ~B(n,p), where n is known but p is UNKNOWN. It is also known that a for known value of x, CDF(x) = Pr(X<=x) = 0.9 Is there anyway to estimate p? To give a concrete example, if n=8...

Homework Statement Find an approximation of (0.99)5 using the first three terms of its expansion. 2. The attempt at a solution To get to the binomial theorem I divided 0.99 into (0.99)5 = (1-0.01)5 = {1+(-0.01)}5 Then, T1 = 5C0(1)5 = 1 x 1=1 T2 = 5C1(1)5-1(-0.01)1 = 5x1x...

Hey all. I have posted a thread regarding this question a while back. I did get an answer and everything. (Here is my old post along with the original question if you are interested: https://www.physicsforums.com/showthread.php?t=592885). So i tried doing that problem again like this: Given...

Homework Statement From the text: Use Hershey's Kisses to estimate the probability that when dropped, they land with the flat part lying on the floor. How many trials are necessary to get a result that appears to be reasonably accurate when rounded to the first decimal place? Homework...

for a non nagative integer $n$, If $\displaystyle I_{n}=\int_{0}^{1}\binom{x}{n}dx$, then $I_{n}=$ where $\displaystyle \binom{n}{r} = \frac{n!}{r!.(n-r)!}$

Use Binomial Theorem and appropriate inequalities to prove! Homework Statement Use Binomial Theorem and appropriate inequalities to prove 0<(1+1/n)^n<3 Homework Equations The Attempt at a Solution So I started by.. \sum ^{n}_{k=0} (n!/(n-k)! k!) a^{n-k}b^{k} = n!/(n-k)!k! (1)^{n-k}...

Hi, Carry out a chi-squared test for the following table of frequencies of X ∼ Binomial(5,p) variates when (a) p = 0.3 x 0 1 2 3 4 5 Observed 162 346 303 149 36 4 frequency Now I know how to carry out the chi-squared test once I have...

Homework Statement I've attached the questionHomework Equations Pr(X<=x)= (x + 0.5 - n*p) / sqrt(n*p*(1-p))The Attempt at a Solution okay so n=1150, p=0.02 , Pr(X<23) =23 + 0.5 - 1150(0.02) / sqrt(1150*0.02*0.98) =0.105316 is that bit right so far. Because it is less than i thought x...

Hi, I've been working on this question which asks to show that {{P}_{n}}(x)=\frac{1}{{{2}^{n}}n!}\frac{{{d}^{n}}}{d{{x}^{n}}}{{\left( {{x}^{2}}-1 \right)}^{n}} So first taking the n derivatives of the binomial expansions of (x2-1)n...

A bag contains 4 red, 5 blue and 6 green balls. The balls are indistinguishable except for their colour. A trial consists of drawing a ball at random from the bag, noting its colour and replacing it in the bag. A game is plated by performing 10 trials in all. At the start of the tournament...

If X and Y are binomial random variables with respective parameters (n,p) and (n,1-p), verify and explain the following identities: a.) P{X<=i}= P{Y>=n-i}; b.) P{X=k}= P{Y=n-k} Relevant Equations: P{X=i}=nCi *p^(i) *(1-p)^(n-i), where nCi is the combination of "i" picks given "n"...

Hi guys, I can't get my head around this, if anyone could help that would be great. "A robotic assembly line contains 20 stations. Suppose that the probability that each individual station will fail is 0.3 and that the stations fail indepen- dently of each other. Given that at least one...

(1+x)^n=1+nx/1!+(n(n-1) x^2)/2!+⋯+ what are the last few terms of this ? I looked and tried but don't seem to get any textbook answer for this.

Homework Statement (1+n)^n≥ 5/2* n^n- 1/2* n^(n-1) for n≥2 Homework Equations i know I have to use this formula (1+x)^n=1+nx/1!+(n(n-1) x^2)/2!+⋯ The Attempt at a Solution And you take x=n from my original inequality but after that I have no clue (1+n)^n=1+n/1! n+(n(n-1) n^2)/2!+⋯ but it...