Statistics Definition and 998 Threads

Homework Statement (a) Suppose a fair six-sided die is rolled once. Let A be the event that an even face occurs and B be the event that a face less than 4 occurs. Are the events A and B independent? Show this mathematically. (b) A fair coin is tossed three times. Let A be the event that the...

Question: So I hold a Bachelor's degree in Chemistry and have just started a M.S./Ph.D. track in Chemical Engineering. My dream job is in mineral processing (the biggest dream is with an asteroid mining company), but I understand that the school I'm going to is heavily focused on drug discovery...

Hello. I have a question about a step in the factorization theorem demonstration. 1. Homework Statement Here is the theorem (begins end of page 1), it is not my course but I have almost the same demonstration : http://math.arizona.edu/~jwatkins/sufficiency.pdf Screenshot of it: Homework...

I am trying to better understand the concept of second order coherence G2(τ) (in particular G2(0)) and a few questions have arisen. Note that I am trying to get a physical idea of what is happening so I would appreciate it if your responses can keep the math to the minimum possible. :) How do...

Hi everyone I have a quick question about independent and dependent variables. Homework Statement The following data set gives the number of miles traveled, and the travel time in hours for each of the 10 car's driving assignments. Miles Time 90 9 40 5 90 9 90...

Currently I am studying a double major in Math and Physics, hopefully leading towards experimental physics, however come next semester I will have to pick my math "specialisations" from two of applied math (mostly chaos and optimisation etc.), pure math(mostly abstract algebra and analysis) and...

Following the "enormous success" (it received a single like) of the last riddle, I decided to waste some bandwidth with a sequel! This one doesn't have an interesting concept or an unexpected solution, it's just hard to solve, so if you're looking for such a riddle, do yourself a favor and...

Here is a short (and old) TED talk where a mathematics professor suggests we teach stats and probability in depth before teaching Calculus because it's math that is more relevant to a wider range of people. Have we got our math curriculum wrong? Thoughts?

I'm reading "Time Series Analysis and Its Applications with R examples", 3rd edition, by Shumway and Stoffer, and I don't really understand a proof. This is not for homework, just my own edification. It goes like this: Σt=1n cos2(2πtj/n) = ¼ ∑t=1n (e2πitj/n - e2πitj/n)2 = ¼∑t=1ne4πtj/n + 1 + 1...

If we're having a thread about probability theory, then we must have one on statistics too! The following questions are all very open-ended and thus multiple answers may seem possible. Your goal is to find a strategy to find the answer to the questions. Furthermore, you must provide some kind of...

Hi there, I've recently start learning methods for determining whether or not time series are stationary. The first method I'm trying to learn is the 'Dickey-Fuller Test'. This test uses a time series modeled by an AR(1) process. The key is to find whether or not this process contains a unit...

I am not sure this is the right forum for this -- I have a question about a particular paper: http://www-users.cs.umn.edu/~sboriah/PDFs/ChandolaCBK2009.pdf The authors describe 4 heuristics that can be derived from categorical data -- this is in order to map categorical data to numerical...

Suppose that a given population is endowed with a pair of characteristics T and K. Let's think of these characteristics as random variables (T,K)∼BiNormal((μT,μS),(σT,σS),ρ) I observe the realisations of T for a sample consisting of those individuals with K<a, where the selection threshold a...

Homework Statement I'm having trouble understanding setting up a frequency distribution. I am confident I am doing it right, but the book I'm using differs when calculating width. The problem gives a bunch of numbers representing the number of counties, divisions, or parishes for each of the...

Right now I'm having a problem with a statistics problem. More specifically with a binomial distribution problem. The problem says: There is a family composed by 8 children. Calculate the probability that 3 of them are girls As far as I know, binomial distribution formula says...

I'll try to be concise. I've been out of math for years and never truly learned to understand it. Until now. I want to put the growth mindset theory to the test and see if I can handle physics (or any STEM field) on a university difficulty. To verify if I'm up to it and even have the slightest...

Homework Statement We have three groups, group 1 contains 21 people, group two contains 18 people and group 3 contain 50 people. First we need to construct a team of 4 people of three groups. How many ways can such a team be constructed? I use combinate such that it will be calculated in...

I'm searching for Bose's paper/article that was published by Einstein. Can someone give me direct link to it ?

This is a question about transforming a probability distribution, using the blackbody spectrum as an example. Homework Statement An opaque, non-reflective body in thermal equilibrium emits blackbody radiation. The spectrum of this radiation is governed by B(f) = af3 / (ebf−1) , where a and b...

degeneracy,this word appears in my textbook many times,but i could not understand what it means in quantum statistics.also in my textbook it is said in bose-einstein statistics that " the deviation from perfect gas behaviour exhibited by bose-einstein gas is called gas degeneracy".but i can't...

Please help me, I will really appreciate it! 1) You are dealing a standard hand of 5 card stud, 1 card face down, 4 face up. Ignoring the cards dealt to all other players what is the probability of you drawing a 9, a heart, and a 9 of hearts assuming you have the 6, 7, 8 and 10 of hearts...

Often in empirical studies you see statements that factor X explains some fraction of the variance in some other variable V, and thinking about what this means intuitively made me curious about the following question. Suppose you have a model where the values of some set of factors X1, X2, ...

Hello everyone. I have been given a problem in my Introductory Mathematical Statistics class. Been thinking about this one for a while and I am simply stuck. 1. Homework Statement "There has been found a DNA of type S on a crime scene. We will assume a total population of N = 5000000 that are...

Hello, I am looking to learn statistics. What would be a good rigorous statistics book for someone who is completely comfortable with proofs?

After the fourth test, Kenny's average mark rises by 5 points, but after the fifth test, it drops by 9 points. If his total score in the last two tests is 122 points, How many points does he score in the last test?

Hello, I was hoping someone could help explain how to do this problem. I have been stuck on it for a while now. I know that you have to use a binomial with n=100, then n=1000 but I'm not sure how to set it up to solve for a range from 8-12%. Thanks! Any advice is appreciated. Also, for people...

Hello, I was hoping someone could help explain how to do this problem. I have been stuck on it for a while now. Thanks! Any advice is appreciated. Also, for people just out to block questions, I AM NOT ASKING FOR THE ANSWER - I AM NOT TRYING TO CHEAT. I just would like help. A hospital receives...

Homework Statement I am given a numerical example (to be solved with pen, paper and calculator only) of an RBS spectrum of a AuAgCu-alloy on a glass-substrate. The question is "Can you get the composition? How accurate is the result?Homework Equations All the Rutherford Backscattering...

Hi there, I'm one of those rare undergrads happy with the idea of being a statistician, although I originally planned to focus on genetics. My mathematical ability and understanding is only at 1st year level, but it improves by the day! I am particularly interested in learning Mathematica and...

Homework Statement Homework Equations $$ Z(1) = \sum_{i=1}^{} e^{\frac{E_i}{K_bT}} $$ where ##E_i## is each of the possible energy states available to a single link (in this case the right and the left states). $$ P=\frac{\sum_{i=1}^{} e^{\frac{E_i}{K_bT}}}{Z} $$ The Attempt at a Solution...

Hi All, Just curious about the techniques used by current political candidates to determine potential voters. I can think of many-variable logistic regression, say, age, years of education, goes to church at least once a month (yes/no), etc. Do they use anything else? Thanks.

In my opinion, math is an exact science, while statistics is an art. Math: perfect Stats: estimation In my opinion, there has to be a difference between the population of mathematicians and statisticians. Mod note: Removed the poll, which isn't allowed in the technical sections.

Hi everybody, I have a statistical problem in interpreting the index The variables for different indicators are taken from different population distributions and they might be recorded in different units of measurement. The values of these indicators are not quite suitable for combined...

Hello Forum, I am taking a lab and we are learning about measurement and uncertainty. Suppose we have to measure the length L of an object. Once the data has been collected we can calculate the mean (average) and the standard deviation s. The resulting measurement would be expressed as [ mean...

Say I have a 0-10 lbf load cell that can measure the force it takes to lift an object. The load cell is accurate to 1% of the full scale. I take 5 measurements and get the following readings: 5.2, 5.1, 4.9, 5.0, & 4.8, all in lbf. Now I am asked to give the mean with the associated...

Homework Statement Hello all, I have a one number stat: Xi 2 4 5 6 6 8 10 Tchebycheff : It ask me to find the value of K. Interval of confidence: 89% I know 1-1/k2 I have no idea how to calculate the value of K. Do I have to somehow use the interval of confidence? I checked my book and...

I heard a guy mention in a debate that some math calculation didn't obey Gaussian statistics. It was a debate re: the economy (not important here, though). I was curious what was meant by "Gaussian statistics" and would appreciate if anyone could offer a sort of layman's definition. Thanks...

I wasn't sure where to post this, but I figured this would be a topic under General Physics. I am aware that the next generation of observations, ranging from cosmological observations to post-LHC particle physics experiments, will produce overwhelmingly large and complex datasets, far larger...

Hi, I have a doubt on the statistics of this game, maybe more philosophical than mathematical. I assume most people are familiar with the game. Suppose you categorised the prizes into 'good' and 'bad'. The contestant plays a very lucky game, and halfway through the game is left with no bad...

Not sure if that's the technical name, but I refer the the number Excel give you between 0 and 1 when you use the "correl" command on two sets of numbers.

Hello... I have a quick assignment for my statistics course, just calculate the mean, standard deviation etc.. We have our choice to calculate these statistics on any data set, anyone know of some cool physical science data, that would be quick to manipulate.. ASCII txt file please :D

Homework Statement One month the actual unemployment rate in France was 13.4%. If during that month you took a SRS of 100 Frenchmen and constructed a confidence interval estimate of the unemployment rate, which of the following would have been true? A) The center of the interval was 13.4. B)...

Inexperienced data analyst here with a real-world example, I have attached a zip-file with screenshots and p-values of the following data. The "reference regions" are Cerebellum White, Cerebellum Gray, and Temporal Cortex. The top-most graphs depict the curves in the indicated region for young...

Homework Statement The problem I have been set is to rework the Drude model using clearly defined scattering statistics. Homework Equations The Drude model as we have been given it is in terms of momentum \vec{p}(t+dt)=(1-\frac{dt}{\tau})(\vec{p}(t)-q\vec{E}(t)dt)+(\frac{dt}{\tau})(0) Where...

Homework Statement An engineer is measuring a quantity q. It is assumed that there is a random error in each measurement, so the engineer will take n measurements and reports the average of the measurements as the estimated value of q. Specifically, if Yi is the value that is obtained in the...

Homework Statement The number of customers visiting a store during a day is a random variable with mean EX=100and variance Var(X)=225. Using Chebyshev's inequality, find an upper bound for having more than 120 or less than 80customers in a day. That is, find an upper bound on P(X≤80 or X≥120)...

Homework Statement Let X∼Geometric(p). Using Markov's inequality find an upper bound for P(X≥a), for a positive integer a. Compare the upper bound with the real value of P(X≥a). Then, using Chebyshev's inequality, find an upper bound for P(|X - EX| ≥ b). Homework Equations P(X≥a) ≤ Ex / a...

Homework Statement Let X1 and X2 be independent normal random variables, distributed as N(μ1,σ^2) and N(μ2,σ^2), respectively. Consider a random variable U = 2X1 − X2. (a) Find the mean of U. (b) Find the variance of U. (c) Find the distribution of U. The Attempt at a Solution a) E(U) =...

Homework Statement If M[X(t)] = k (2 + 3e^t)^4 , what is the value of k Homework Equations M[X(t)] = integral ( e^tx * f(x) )dx if X is continuous The Attempt at a Solution I tried differentiating both sides to find f(x), but since it is a definite integral from negative infinity to infinity...

One hundred pennies are being distributed independently and at random into 30 boxes, labeled 1, 2, ..., 30. What is the probability that there are exactly 3 pennies in box number 1? I tried using a Poisson distribution f(x) = (e^-λ)*(λ^x)/x! , with λ = 100/30 = 10/3 and x = 3. I got 0.22021 (5...