Statistic Definition and 122 Threads

Three conditions must be met in order for the Poisson Distribution to be used: 1) The average count rate is constant over time 2) The counts occurring are independent 3) The probability of 2 or more counts occurring in the interval $n$ is zero Simply, why must these conditions be met for valid...

hey folks, My question is how to find probability of getting 3 CONSECUTIVE heads or more in 20 coin flips, what are the odds I have an approach which I need to verify and please clarify in case of missing points. No. of possible outcomes = 2 ^ 20 first I assume that first 3 outcomes are...

I have a physical quantity A defined as ##A=(74.5 B^2*(M+N))^{1/3}## where B, M, N and relative uncertainties are given. And M and N are dependent on B. Could you show me how to calculate and estimation for the uncertainty on A? Thanks a lot

I'm looking for papers or other references on DNA profiling statistics. Something comprehensive that covers the whole shebang. I kind of troubled by some of the match probabilities being linked to "race" i.e. Caucasian. I'm not even sure what Caucasian even means scientifically. What happens...

I was studying in my math textbook about these two methods to measure dispersion and variability in data. I was able to understand mean deviation that it's the average by how much a quantity deviates from mean but I was unable to understand standard deviation. Also, as standard deviation squares...

Hello, I am trying to understand the intuition of the definition of the period of a state in a Markov chain. Say for example we can go from state i to state i in 3,5,7,9,11... and so on steps. The gcd here is one. So is this aperiodic state or one with periodicity of 2. Thanks

Let $\underline{X}=X_1,...,X_n$ an random sample of size $n$. Show that the statistic $T=\displaystyle\sum_{i=1}^n X_i$ is an sufficient statistic for $p$ if $X\sim Bernoulli(p)$ with $0<p<1.$ Hello :). I think that can use the Fisher Theorem (Factorization) for find the statistic and...

How to prove this "if p(a)=p(b)=p then p(ab) ≤ p^2Homework EquationsThe Attempt at a Solution

Looking at another textbook problem, hope someone can let me know if I'm on the right track: Let $X_1, X_2, ... X_{25}$ be a random sample from some distribution and let $W = T(X_1, X_2, ... X_{25})$ be a statistic. Suppose the sampling distribution of W has a pdf given by $f(x) =...

There are around 7.000.000.000 people in the world.There are around 60.000.000 deaths a year. 1.000.000 commit suicide every year.What is right to assume- That 1 out of 7.000 people commit suicide or 1 out of 60 people commit suicide? I am having a hard time with that. Could someone help me?

Let's suppose i have a class of interval 7, say [20, 27[ With the numbers 20 21 22 23 24 25, there are 2 ways to derive the median yes? I may use [a+b[ /2 to get the median which in the case above will give me 23.5, or i may simply look at the numbers above and clearly see the median is...

Homework Statement Let Yi∼iid,uniform[0,θ]. Let U=max{Yi}. Derive the distribution of U and give the value of any associated parameters. Also calculate E(U) and Var(U). Homework Equations f(y)=1/Θ and F(y)=y/Θ The Attempt at a Solution Since we have a product of iid random variables, we can...

Is this a correct conclusion from these three facts ? One in five cigarette smokers dies from smoking. There are about 45, 000,000 smokers in the U.S. There are about 450,000 smoker deaths/year from their smoking habit. So 450, 000/45,000,000 = 1% . So if the number of smokers (45,000,000/yr)...

Hey all, I'm doing some research on protein dynamics which involves fitting models to data. Basically, we think that our system can be described by a complex, 5 parameter model rather than the generally accepted 2 parameter model. The data we're working with was acquired from experiments where...

Hi, friends! Since this is my first post, I want to present myself as an Italian who is trying to teach himself mathematics and natural sciences, while having a strictly humanities-centered school background, and I am tempted very much to enrol in a university scientific course. I read in the...

Hi! I was wondering In my note we've a Corollary saying: If T is sufficient for \Theta, the maximum likelihood estimate is a function of T. where T is T(X_1,X_2,...X_n) and X is given by f(x|\Theta) I was wondering, isn't every Maximum likelihood estimator a sufficient statistic?Thanks for...

Homework Statement Calculate entropy for density matrix with eigenvalues ##0## and ##1##. Homework Equations ##S=-\lambda_1 \ln \lambda_1-\lambda_2 \ln \lambda_2## where ##\lambda_1## and ##\lambda_2## are eigenvalues of density matrix. The Attempt at a Solution How to calculate...

Homework Statement Homework Equations So far I have only worked on question 1, as I was not able to solve it. The likelihood ratio test statistic is defined as follows: λ = 2 Log(L(theta-hat)/L(theta-hat_0)) Where L is the likelihood function, the product of all the pdfs/pmfs, and theta-hat is...

I am confused by the labeling of the (only) graph in http://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test The values on the vertical axis appear to be the values of 1-(the chi-squared cumulative probability distribution values*) as I would expect in finding the p-values. However...

Homework Statement When calculating the P-value, must you change the sign of the test statistic depending on the type of test (lower, upper)? For example, if your calculated test statistic is t=2.5 and you want to perform a lower-tailed test, is your answer the cumulative probability of...

Homework Statement An infinite-length binary text create from these patterns, with probability: "0": 0.8 "11": 0.1 "100": 0.05 "101": 0.05 ( For example: 0111001001010 ("0" "11" "100" "100" "101" "0") is a valid excerpt from the text) I temporary call a,b,c,d for P("0"), P("11"), P("100")...

Let's assume there's a magical ball that bounces once every .5 seconds, and that there was a specific machine designed to calculate the rate of the ball's bounce (with error). After performing numerous readings of the ball's bounce using this machine, you have a collection of values describing...

Homework Statement Forced expiratory volume (FEV) is an index of pulmonary function that measures the volume of air expelled after 1 second. FEV is influenced by age, sex and cigarette smoking. Assume that in 45- to 54-year-old nonsmoking men FEV is normally distributed with mean = 4.0 L and...

'Ello, I have a question regarding the results in this paper (and another which I will mention later) http://arxiv.org/abs/hep-ph/0212199 Now, I'm not so concerned about the 'braney' bit, but more their definition of the cross section in Eqn. (46). They have included the usual (2j+1)...

Hello all, I got stuck with some problem of probability What I understand is how to verify by statistics, that a die (is that really the singular of dice ??) is crooked: - cast it a number of times, say twenty - count the number that shows most, say we find eight times the six -...

Hey everyone! Exam practice, that time of year. In this problem 13 with correct answer C, I'm not sure how they get the test statistic: http://i.imgur.com/doar3.jpgI think they want you to use a F-test, that tests the entire model, which is calculated by: F= ((R^2)/ K)/ ((1 - R^2)/(n-K-1))...

being stuck by standard deviation, I just can't understand the difference between n and n-1. who can give me some concrete examples? thank you!

μHomework Statement Let X1...Xn be a random sample of size n from a normal distribution, Xi~N(μ, sigma^2), and define U = ƩXi and W = ƩXi^2. Find a statistic that is unbiased for δ^2 + μ^2 in terms of U and W. Homework Equations xbar (sample mean) = Ʃxi/n S^2 (sample variance)(Ʃxi^2...

I have calculated the one sided t-test statistic and am getting a negative value as the sample mean is less than the mean under H_0. there are no negative t values in the table - do i take the absolute value of this? thanks

In my exploration of energy storage options i came across a statistic several times that given a vacuum and magnetic bearings, a flywheel can achieve 97% storage efficiency. Whether its true or not, what does 97% represent? Does it imply that the energy will hold regardless of time and its a...

Question regarding this statistic: I've read on here a lot that if you complete a physics PhD you have a 1 in 10 chance of obtaining a research professor job. 1 in 4 chance if you graduate from a top school. This is after an average of 6 years of postdoc'ing (for the top school, 1 in 4...

Can anyone come up with an intuitive explanation or point me to a link that gives a derivation of the test statistic in chi-square test? I am having problems understanding why the particular test statistic is approximated by a Chi-Square random variable under the null hypothesis of the...

Badly need help to attempt this question because i am 90% sure a question like this will appear in the exams that i will be taking next week. Find out how many 3 digit odd number that can be obtained form digits 1, 2, 3, 4, 5, 6, 7 if 1/ repetition of digit not allowed 2/ Repetition of...

How many times will the number 3 appear in counting numbers from 1 to 1000? PS: Just joined the forums.

Hi, I've been trying to get my head around z and t statistics. and I almost have a matra in my head that "when the sample are small, use the t test, when the samples are big, use either the t or the z test". Now As I understand it, the z test requires a large number of samples, because it...

Hey All, Can someone please explain to me why the p value is obtained by taking the integral under the z curve from the z statistic you calculate to the end of the tail ? Thanks

Hello there, I am a medical student and I would like to discuss a slightly confusing question that I got in a certain examination. Here it is: A researcher wanted to study the association between breast cancer and oral contraceptive use. She selected 50 women diagnosed with breast cancer and 50...

Hi, Can someone kindly explain a bit on the 'red' part. I have tried to search for it, but nothing much related seem to come out. You may not tell me what it is, all I need is some related resource ( section in a book, or a website, or an article? ) Thanks.

So, I am discussing with a friend of mine the odds of having a team be involved in a season end tiebreaker 2 years in a row. Although I did have statistics in college, I am a not a great statistician, so I am wondering if someone can help me with how to calculate the odds. Thanks!

Well, first i will have to make an apology for putting the question in this forum, but was not really sure where else i could put it. :) The assignment is: The number of oil tankers, arriving at a certain refinery on one day, follow a poisson distribution with the parameter µ=2. The present...

I haven't touch statistics for year and now I came back to find I am totally lost. Here is one of the question that I wish to know how to solve it, in terms of steps, so that I can gain back memory about it. I know it is a bit too much, but I am really very very lost and depressed, help.

Homework Statement Expect that some of the generated random digits will repeat because the trials are independent. You need a large amount of data (random digits), so pool your data with other students who have the same calculator version as you. Advertise for collaboration on the...

I went for a lecture and the lecturer said that the square of the difference between the x sub i and the mean is the take precaution of the negative value. This has been bugging me , i was wondering why don't they just take absolute because there is a difference between ...

Homework Statement how to do with the normal distribution if the mean is not 0 variance is not 1. for example p(x>1) if x-N(2,3) ? Homework Equations The Attempt at a Solution

Homework Statement System of weakly interacting particles in equilibrium temperature T, each particle can exist in three energy states -epsilon, +epsilon and 0. There are three times as many particles in the -epsilon state as in the +epsilon state. Show that fraction of particles with energy...

Hi all. I'm struggling with this HW question. I've searched through the textbook and on the web and have been unable to find a solution Homework Statement I've got 4 i.i.d. random variables, X1, X2, X3, X4. Uniformly distributed on [0,1] so the pdf = 1 and cdf F(x_i) = x_i Let Y3 = the third...

Homework Statement Due to the expense involved, car crash tests often use small samples. When 5 BMW cars are crashed under standard conditions, the repair costs (in dollars) are as shown in accompanying list. Use 0.05 significance level to test the claim that the mean for all BMW cars is...

Hi! I'm on my way to get my bachelor in Statistic and mathematic with specialization in statistic...the thing is i heard a few people said that they have to go back to school because this field has no future...Now I'm kinda worry because I'm not sure if I'm in the right field. I like doing what...

Homework Statement In an ancient culture, the average male life span was 37.6 years, with a standard deviation of 4.8 years The average female life span was 41.2 years, with a standard deviation of 7.7 years. use the properties of the normal distribution to find the following: a. What...

Hi all, I've been confused about this for a while. Since it wasn't mentioned in class or my textbook, it probably reflects a fundamental lack of understanding :( With any unbiased estimator, why is the distribution of the estimates also the distribution of the statistic? Eg, suppose...