Binomial Definition and 640 Threads

Problem 1: About 50% of all persons age 3 and older wear glasses or contact lenses. For a randomly selected group of five people find the probability that: a. exactly three wear glasses or contact lenses b. at least one wears them c. at most one wears them For this problem I set n=5...

Have an example: 123455 111555 the sample space is 0..9 row 1 can pick 6 numbers out of which 2 are repeated row 2 can pick 6 numbers out of which 3 by 3 are repeated I want to know what is the real probability that row 1 will match with 2 distinct numbers numbers row 2, and a repeated number...

use the binomial expansion formula to find the alternating sum of the numbers in row n of Pascals triangle. nC0-nC1+nC2... So I wrote a few rows of the triangle and it looks like once you get past row zero the alternating sum of the numbers in the rows all add to zero. Does that work...

I have a list of chemicals, their assay test results, and a binomial column of whether or not the assay test result was high enough to be considered a threat (anything >2g/ml). Some chemicals were tested more than once, but others were not. It is understood that it is a poor set of data, but I...

Hi, could someone possible make something clear for me - I have come across this notation for a binomial PMF formed from an underlying beurnolli distribution: PS_{n}(\bar{p}n)\sim\sqrt{\frac{1}{2\pi n\bar{p}(1-\bar{p})}}exp [n\varnothing(p,\bar{p}] ,\\...

These three quotes talk about the use of the Poisson and normal distributions as approximations for the binomial when n is large. The first two quotes here say Poisson is best when p small, and the normal otherwise. The third seems to change the story; it says Poisson is best for large p too. Is...

Here, to further test my understanding, is an attempt to apply the measury theory definitions of a probability space to the binomial distribution. All comments welcome! Let (R,D,O) be a probability space: R = \left \{ 0,1 \right \} D = 2^R O:D\rightarrow[0,1] \; | \; O(\left \{ 1...

Where did the binomial theorem come from...?

Homework Statement Calculate the following sum: (click to expand)The Attempt at a Solution I tried something with Moivre formula and Newton binomial theorem but no result :redface:, should i continue with these or is there any simpler approach? I just need some hints. Thanks.

Homework Statement I need to sum the binomial coefficients that are divisible by a positive integer t, i.e. \sum_{i=0}^{s}\binom{ts}{ti} Is there any way to get rid of the sum sign? Homework Equations Let t be fixed and s go to (positive) infinity (both t and s are positive...

In a recent federal appeals court case, a special 11-judge panel sat to decide on a certain particular legal issue under certain particular facts. Of the 11 judges, 3 were appointed by political party A, and 8 were appointed by political party B. Of the party-A judges, 2 of 3 sided with the...

Hi, When (1+ax)n is expanded as a series in expanding powers of x, the first three terms are 1 - 8x + 30x2 Calculate the values of a and n. So, I think we need simultaneous equations and I managed to build the first one: a*n = 8 My problem is however, that to construct the second...

Homework Statement If n \in N, then 11n+2 + 122n+1 is divisible by:- a)113 b)123 c)133 Homework Equations The Attempt at a Solution I did it by substituting different values of n and divided by each of the option. Answer came out to be 133. But I want to do it step by step...

Fix some constant 0<\alpha \leq 1, and denote the floor function by x\mapsto [x]. The conjecture is that there exists a constant \beta > 1 such that \beta^{-n} \sum_{k=0}^{[\alpha\cdot n]} \binom{n}{k} \underset{n\to\infty}{\nrightarrow} 0 Consider this conjecture as a challenge. I don't...

If two binomially distributed variables are generated as paired events, how often will the variable with p=X be greater than the variable with p=Y? Also what is the "equity" if ties are counted as .5 for each? For instance in Excel I generated 10,000 numbers with p=.8 and 10,000 with p=.6...

Homework Statement Let X~UNIF(0,1). Find y = G(u) such that Y = G(U)~BIN(3,1/2) Homework Equations The Attempt at a Solution after a bit of searching/reading, i found how to do this with a continuous distribution (the problem i had was an exponential, so i took the inverse)...

Maybe someone is really good with stats, or has access to a statistics professor. Here we go: I am trying to determine the power for a study. The distribution is binomial. I have a device that either works or does not work. I do not know the real probability, but I think it is very good...

I have some data (4 runs each of about 10 trials) which is binomial with n_hits/N_trials n/N = 0/11, 0/9, 0/10, 0/10 So, I estimate the probability p = n/N = 0 But how can I calculate an uncertainty on this value? I thought to try total N_tot=40 and n_tot=1, so p_tot=1/40 = 0.025 (i.e...

Homework Statement Find the coefficient of http://webwork2.math.utah.edu/webwork2_files/tmp/equations/73/3e29a3b979c709dbb6c609c5a6ce891.png in the expansion of [PLAIN][PLAIN]http://webwork2.math.utah.edu/webwork2_files/tmp/equations/63/dcb58790e8122dce61b830977294091.png Homework Equations...

Homework Statement A car dealer estimates that 50% of customers entering the dealership will buy a normal car, 20% will buy a high-end car, and 30% are just browsing. If 5 customers enter his dealership on a particular day, what is the probability that two will purchase high-end models, one...

I am trying to predict the modulus without really doing the expansion. Therefore I'm in a snag with actually computing vs. only computing what I think I need. Here's the assumption I am Making: n C r == 0 mod (n-1) for all r > 1 n C r are the coefficients of the binomial expansion. My...

Hi members, Hope someone can help with this assignment question? I need to proof: E(1/1+X) = [1-(1-p)^n+1]/p(n+1) where X ~ Bi(n,p) Below are my steps and I'm not sure where I went wrong: 1. sum(x=0 to n) (1/1+x)*(n choose x)*p^x*(1-p)^n-x 2. sum(x=0 to n)...

Electric Dipole and Electric Potential.. and binomial approximation! Homework Statement An electric dipole at the origin consists of two charges +q and -q spaced distance s apart along the y-axis. a.)Find an expression for the potential V(x,y) at an arbitrary point in the xy-plane...

Homework Statement by expanding the binomial show that ( (Sqtroot(3)/2) + (1/2)i )^4 = ( (-1/2) + (sqroot(3)/2)i ) The Attempt at a Solution I'm stuck, I now ( (Sqtroot(3)/2) + (1/2)i )^4 = ( (9/16) + (1/16)i ) But that's all I got, don't know the next steps.

What is acceptable summation notation for a binomial expansion of, for example (1+x)^n, from the zeroth to the (n-1)th term? For example a possible expansion maybe (1+x)^4, where by I would like to write in summation notation that the expansion would be : 1 + 4x + 6(x^2) 4(x^3) . Notice...

Homework Statement Prove that , if x is so small that terms in x3 and higher powers may be neglected, then http://www.mathhelpforum.com/math-help/attachments/f37/21081d1299568824-binomial-expansion-question-msp520319eed9935g5h93hf000055b8ic10787h09a9.gif . By substituting a suitable value of x...

Homework Statement Find the coefficient of x5 for the expression: (1-x)6(2x+3)4 The answer provided is -222, but my answer is far from that, can any enlighten me? Homework Equations The Attempt at a Solution

Hi there, As many texts' discussion, we usually use a variable x for any value randomly picked. For a Bernoulli trials, i.e. each random variable x can either be successful or fail. If the probability of success if p and that of failure is q=1-p, then the expectation value of x would be...

Help! Binomial Distribution: Statistics for M.E's Homework Statement Four wheel bearings are to be replaced on a company vehicle. The mechanic has selected the four replacement parts from a large supply bin in which 10% of the bearings are defective and will fail within the first 100 miles...

Hello, I considered a Binomial distribution B(n,p), and a discrete random variable X=\frac{1}{n}B(n,p). I tried to compute the characteristic function of X and got the following: \phi_X(\theta)=E[e^{i\frac{\theta}{n}X}]=(1-p+pe^{i\theta/n})^n I tried to compute the limit for n\to +\infty...

Homework Statement find the characteristic equation of a binomial variable with pmf p(x) =\frac{n!}{(n-k)!k!}*p^{k}*(1-p)^{n-k}Homework Equations characteristic equation I(t) = \sump(x)*e^{tk}The Attempt at a Solution I(t) = \sum\frac{n!}{(n-k)!k!}*(p^{k}*(1-p)^{-k}*e^{tk})*(1-p)^{n} i am...

Homework Statement The Attempt at a Solution Is there any difference between the above expression and ? Is there any relation between these two?

Homework Statement Let k >= 3 be any integer. What is the probability that a random k-digit number will have at least one 0, one 1 and one 2? (as usual every number starts with either 1,2,...9 and NOT zero) Homework Equations b(x : n,p) = (n x)p^x*(1-p)^(n-x) where x = 0, 1, 2, ... ,n...

Homework Statement The question provides a table and asks: Number of Attempts Fraction persisting in fibrillation 0 1.00 1 0.37 2...

Homework Statement Find and prove a formula for sum{ (m1 choose r)(m2 choose s)(m3 choose t) } where the sum is over all nonnegative integers r, s, ant t with fixed sum r + s + t = n. Homework Equations The Attempt at a Solution I first attempted to find the number of combinations of r...

Homework Statement Prove that for an integer n greater than or equal to 2, nC1 - 2nC2 + 3nC3 - + ... = 0. (nCm means n choose m) Also, 2x1 nC2 + 3x2 nC3 + 4x3 nC4 +... = n(n-1)2^(n-2) Homework Equations (1+t)^a = 1 + aC1(t) + aC2(t^2) + ... The Attempt at a Solution I don't know...

Is there a way to calculate, say, the probability of a dice landing on an 11, given that the binomial probability of getting exactly six elevens in 100 tosses is 24.6%?

How to calculate 1) binomial coefficients and 2) binomial distribution on a Casio fx-9860G calculator?

Homework Statement Prove that \sum^{l}_{k=0} n \choose k m \choose l-k = n+m \choose l Hint: Apply the binomial theorem to (1+x)n(1+x)m Homework Equations The Attempt at a Solution I apply the hint to that thing to get \sum^{n}_{j=0} n \choose j x^j \sum^{m}_{k=0} m \choose k...

can anyone help me please can anyone solve this problem for me please Q) The Binomial distribution allows the calculation of the probability of k successes in n trails where there are only two outcomes: success or fail with probabilities p and q respectively. The Binomial probability is...

Using summation((\stackrel{n}{k})xkyn-k) = (x+y)n, I let x = y = 1. This should then result in summation((\stackrel{n}{k})*1*1) = (1 + 1)n = 2n. Expanding the summation, I get (\stackrel{n}{0}) + (\stackrel{n}{1}) + ... +(\stackrel{n}{n}) = 2n. Solving this results in...

On a production line, only 45% of items produced meet quality standards. A random sample of 500 items will be taken. Using the normal approximation to the binomial distribution, approximate the probability that less than half of the sampled items meet quality standards. 500*.5 = 250...

Homework Statement 10% of engines manufactured on an assembly line are defective. If engines are randomly selected one at a time and tested, what is the probability that the first defective engine will be found between the 5th trial and the 25th trial, inclusive? Homework Equations...

Prove for all n\inN 2n= (\stackrel{n}{0})+(\stackrel{n}{1})+...+(\stackrel{n}{n}) So I used mathematical induction base case: n=0 so 20=1 and (\stackrel{0}{0})=1 induction step: Let n\inN be given, assume as induction hypothesis that 2n=...

Homework Statement Prove that (1 + 1/n)^n = 1 + \sum1/m!(1 - 1/n)(1-2/n)...(1-(m-1)/n) where our sum is from m=1 to n. 2. Attempt: I recognize the binomial theorem here, but I'm having a mental block in how to figure this out. I should know how to do this, I think I just need a little help...

Hi guys, I'm Filip and as a 11th grade student I have a question about one mathematical problem. It says: If the coefficient of xk in the expansion of (3+2x-x2 )*(1+x)34 is zero. Find the value of k. I know it's something related with binomial theorem, but I don't really know how to start. Thank...

Hi... Hope i 'll get the good result that where we practically use the binomial and poisson distribution in the field of engineering...

Homework Statement There is a derivation in the text that I'm having problems replicating. The text gives the formula for tidal potential as: U_{tid}=-GM_{m}m(\frac{1}{d}-\frac{x}{d^{2}_{0}}) Where M_{m} is the mass of the moon, d is the distance from the CM of the moon to the point of...

I'm learning the subject of electric fields from Resnick and Halliday's book, and they have an equation for the field of the dipole: E = \frac{1}{4\pi\epsilon_0}\frac{p}{x^3} \left[1+\left(\frac{d}{2x}\right)^2\right]^{-3/2} Their next step is to find out what happens when x is larger than...

Homework Statement Use mathematical induction and Pascal's Identity to prove: \binom{n}{0} - \binom{n}{1} + \binom{n}{2} - ... + (-1)^{k}\binom{n}{k} = (-1)^{k}\binom{n-1}{k} The Attempt at a Solution First, I guess this means something like: \sum_{i=0}^{k}(-1)^{i}\binom{n}{i} =...