Binomial distribution Definition and 142 Threads

Suppose I have 6 die and toss them. The probability to have n 6's is binomially distributed with parameter 1/6. Now suppose instead tossing the 6 die and having 1/6 probability for a 6 each dice's probability to show 6 grows continously in the time interval t=0 to t from 0 to 1/6. Can I then...

This is not a homework problem. Just a curiosity. But my statistics is way rusty. Suppose a binomial probability distribution with probability p for a success. What is the expected number of trials one would have to make to get your first success? In practice, this means if we took a large...

Hello all, I just have a question which covers binomial distribution. Sally is a goal shooter. Assume each attempt at scoring a goal is independent, in the long term her scoring rate has been shown as 80% (i.e. 80% success rate). Question: What's the probability, (correct to 3...

Homework Statement Repeatdly roll a fair die until the outcome 3 has accurred on the 4th roll. Let X be the number of times needed in order to achieve this goal. Find E(X) and Var(X) Homework Equations The Attempt at a Solution I am having trouble deciphering this question...

So I've translated this assignment from another language, but hope it's good enough translated/understandable. Homework Statement According to the Statistics of Denmark, there was in the construction sector in the period 2009-2011 an average of 920 business bankruptcies per year out of a...

Homework Statement In a class with 20 and one with 10 students each student has a probability of 0.3 to not show up on a particular day. On a given day, which class is most likely to have the highest ratio of absent students? This was in my exam, unfortunately I did not know how to do it...

1. The problem statement Consider the Binomial Distribution in the form P_{N}(m)=\frac{N!}{(\frac{N+m}{2})!(\frac{N-m}{2})!}p^{\frac{N+m}{2}}q^{\frac{N-m}{2}} where p+q=1, m is the independent variable and N is a parameter. Show that it satisfies the marcoff chain...

The prices for bananes that a fruit shop would have to pay to keep them in stock have a mean of $1.35/kg and a standard deviation of 18 cents. The owner will not pay more than a certain price, but manages to keep stock 8% of the time. What is the maximum price the ownwer will pay? I found...

Greetings to you, Physics Forums regulars! Please allow me to introduce myself a bit first. I'm a student in the Life Sciences, so I don't really have a lot of knowledge on mathematics past the basics. I'm not sure if my problem belongs here. This is my first visit to this...

Hi, I am new here, and my name is Jonas. I'm a CS major at a university in the Northeast US. I'm a senior and wrapping up degree requirements which include a science track. I chose Chemistry because Physics was full. The chemistry exams are multiple choice (because you couldn't grade 300...

I'm looking through my statistics notes and on the page that's giving examples of cases where you can use a binomial distribution it gives the problem: "The number of red counters in a randomly chosen sample of 30 counters taken from a large number of counters of which 10% are red." Now...

Homework Statement A fair coin is tossed 491 times. The total number of heads or tails is then even or uneven. Is the probability that the head will result in an even result equal to 1/2 Motivate your answer with a strict mathematical proof. Homework Equations I am having some trouble...

Homework Statement Of all the weld failures in a certain assembly, 85% of them occur in the weld metal itself, and the remaining 15% occur in the base metal. A sample of 20 weld failures is examined. a. What is the probability that fewer than four of them are base metal failures...

Hello PF This might be a fairly simple question to most of you, but I was given this problem (don't worry, I already solved it just wondering about something) Suppose the probability of suffering a side effect of a certain flu vaccine is 0.005. If 1000 persons are inoculate, find the...

A pdf is of the exponential family if it can be written $ f(x|\theta)=h(x)c(\theta)exp(\sum_{i=1}^{k}{w_{i}(\theta)t_{i}(x))}$ with $\theta$ a finite parameter vector, $c(\theta)>0$, all functions are over the reals, and only $h(x)$ is possibly constant. I would like to show the binomial...

For binomial distributions, how can you tell which central tendency value (mean, median, or mode) and which variability value (interquartile range, variance, standard deviation, etc.) are most appropriate for the data? Thanks for any reply.

Differences between binomial distribution and "forced" probability distribution Hi everyone. Yesterday I was thinking about probability and real life and about the fact that we always expect life's facts to behave according to probability theory. If we flip a coin and we get 6 times heads...

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.

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...

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 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...

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] =...

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 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...

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...

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...

Suppose you have a coin with 4 fair sides, flip it 5 times, and want to know the probability of 5 heads. This is K(10,5) * (0.25)5 * (1-0.25)5 = K(10,5)*0.255*0.755 Or more generally for any binomially distributed outcome: 1) p(x=r) = pr*(1-p)n-r*K(n,r) But also we must have that: 2) p(x=r)...

Is the binomial distribution, what you call a product distribution? How can I see that, if that is true?

Homework Statement A quality control engineer tests the quality of produced computers. Suppose that 5% of computers have defects, and defects occur independently of each other. A- What is the expected number of defective computers in a shipment of twenty? B- Find the probability of exactly...

Hi there, I'm looking at a problem and wanted some help to advise if I'm going in the right direction. I need to test if the number of times a lotto ball has appeared in a draw fits a binomial distribution. I have collated the data and ultimately will do a hypothesis test. The draw...

Is quite easy to understand. What I don't understand though is this: When you sum over all the binomial probabilities from i=0 to n you should get 1, as this corresponds to the total probability of getting any outcome. I just don't understand what it is, that guarantees that you always get one...

Homework Statement http://puu.sh/epl6 Answer http://puu.sh/eplm Homework Equations The Attempt at a Solution No clue on how to attempt this problem. Any help would be appreciated, thanks!

Homework Statement http://puu.sh/dOcM Answer: http://puu.sh/dOcZ Homework Equations The Attempt at a Solution I got Part A. For part A, this is what I did: I did Egg A: X ~ (6,(1/6)) P(X = 1) and did something similar for Egg B. I then multiplied both to get the answer for Part...

I'm having a bit of trouble understanding a probability distribution of 2 variables. Take for example taking n cards from a deck, and seeing what is the probability of getting X queens and say Y aces (with replacement). This involves the binomial distribution. The probabilities for the...

Hi, An airline knows from past experience that the probability of a person booking a seat and then not turning up is 0.04. A small plane has 50 seats and 55 bookings are made. a) A binomial distribution is used to model this situation. What assumption must be made? Comment on how...

If X is a binom. rand. var., for what value of θ is the probability b(x;n,θ) at max? Ive no idea... My only guess (most likely wrong) is that max and min are always derivatives... So do i just differentiate and express θ...? Any suggestions...?=( Thank you!

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...

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...

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)...

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 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...