Statistics Definition and 998 Threads

typical random walk : one step forward or backward with equal probability and independence of each step , what is the expectation and Variance . so i define indicator variable xi ={1 or -1 with equal probabilty . E(xi) = 0 Var(xi) = 1 now define Sn as the sum of i=1,...,n each step is...

Hello, I would be interested in a collection of experimental data for the Michelson-Morley Experiment . I would like to see if there would be many data available, and if a statistical analysis could be of some fun. Would you know some compilation of data? Thanks, Michel

to begin with I am a biophysicist so my question is very naive. It is my understanding that the Uncertainty Principle deals with a single event (particle). It is also my understanding that quantum physics contains a lot of statistics (probability). The question is: in the area of...

Homework Statement Hello! I'm trying to understand how to solve the following type of problems. 1) Random variables x and y are independent and uniformly distributed on the interval [0; a]. Find probability density function of a random variable z=x-y. 2) Exponentially distributed (p=exp(-x)...

Hi everyone, I recently got a job through my instructor to design labs for a new course we are offering. It is Engineering Statistics for Electrical and Computer engineering. We will be using Yates text. We previously had to take a engineering stats class in the math department that is more...

Hi, I have a very basic statistics homework question, and I have given it a go, but I just wanted to know if I had approached it correctly: QUESTION A shop adjusts its staffing levels using a model of customer demand through the week in the ratio of: 0.22(Mon); 0.14(Tue); 0.16(Wed); 0.18(Thu)...

Suppose that I have these random variables ##\eta_k=\alpha_k/\beta_k## for ##k=1,\,2,\,\ldots,\,K##, where ##\{\alpha_k,\,\beta_k\}## are i.i.d. random variables. Now suppose that I select ##M\leq K## random variables such that denominators are the largest ##M## random variables. That is...

Homework Statement Determine if the classical approximation (Maxwell-Boltzman statistics) could be employed for the following case: a) Electron gas in a metal at 2.7K (cubic metal lattice of spacing 2Å) Homework Equations Maxwell-Boltzman statistics are acceptable to use if the de broglie...

Suppose that ##Y=\sum_{k=1}^KX_{(k)}##, where ##X_{(1)}\leq X_{(2)}\leq\cdots X_{(N)}## and (##N\geq K##). I want to find the characteristic function of ##Y## as \phi(jvY)=E\left[e^{jvY}\right]=E\left[e^{jv\sum_{k=1}^KX_{(k)}}\right] In the case where ##\{X\}## are i.i.d random variables, the...

Homework Statement The back row of a cinema has 12 seats, all of which are empty. A group of 8 people including Mary and Francis, sit in this row. Find the number of ways they can sit in these 12 seats if a) There are no restrictions b) Mary and France's do not sit in seats which are next to...

Hi there, not sure whether this is in the right section but: I've made two runs of a radioactive decay experiment where I've got a log(N) vs. time plots. From this I've got the decay constants and hence the half-life. I've averaged these two half-lives ( = 160 secs) and now I'm trying to work...

Homework Statement Homework Equations All needed are in the picture above (i hope so) The Attempt at a Solution to me it is extremely difficult because it is so complicated with many notations. Also, I actually don't know how to read the question properly to answer it Is E(beta) is the...

Hello everyone, I would be happy if someone explained the small reduced chi squared value to me. I have fitted a set of measured data with an exponential function, which I need for some sw calculations. The fit seams great, the origin sw also provides the reduced chi squared, but it is very...

These ideas come from the book Quantum Physics by Eisberg and Resnick (specifically ch11), can anyone explain what the inhibition factor and enhancement factors are in a little more detail? I do not understand what the book is trying to explain, and I can't seem to find these anywhere online...

Hello! I marked the thread as a basic high school level, because I assume my question is just at that level. ) I am reading some materials on statistics now, and, not having enough background yet, I stumbled upon this sentence: "As an example, 50°C, although five times as large a number as...

Homework Statement Out of all the products a company makes 2% is damaged. During the routine control of the products, the products are put to a test which discovers the damaged ones in 99% of the cases. In 1% however it approves the damaged item as a working one and vice versa. Find the...

Hi at all, maybe it's a bit trivial. However, the question that i ask myself is ; that relation there is between statistics-probab theory & theoretical physics. What role does it play in theoretical research ? (apart from the probabilistic amplitudes encountered in qm) Thanks for the answers

Homework Statement 12 non-distinguishable attacks from President Snow land in Panem’s 12 districts in a particular week. Assume the attacks are located randomly, with each configuration of attacks equally likely. What is the probability that some district had more than 1 attack? Homework...

Homework Statement The actual question was deriving Bose-Einstein, but I got confused on the F-D example. I'm basically following the method given here. Homework Equations [All taken directly from the above link] Taylor series: The Attempt at a Solution So after that third equation...

This thread is for us to discuss the text The Drunkard's Walk: How Randomness Rules Our Lives by Leonard Mlodinow, and by that I mean for me to ask questions of you, those of you who will suffer me, my experts in probability, the PhysicsForums readers, on things I'm interested in from the text...

I find both subjects interesting, to the point where every night after putting the kids to bed, I spend a few hours self-studying, but I wonder if going back for a master's degree would be worth the effort. I know that if I want to do professional work in either of these two subjects I'll need...

Homework Statement two indepedent observations ##X_1## and ##X_2## are made up of the continuous random variable having the probability density function ## f(x)= 1/k##, and ## 0≤x≤k## find a. the cumulative distribution of ##X## b. Find the probability distribution of M, the...

Many textbooks claim that particles that obey Boltzmann statistics have to be indistinguishable in order to ensure an extensive expression for entropy. However, a first principle derivation using combinatorics gives the Boltzmann only for distinguishable and the Bose Einstein distribution for...

There is solid empirical evidence that error in particle physics measurements is not actually distributed in a Guassian manner. Why don't particle physicists routinely use student t error distributions with fat tails that fit the reality of errors in experimental measurement more accurately...

Homework Statement Say I have four categories which make up a "whole" that I'll call a unique "deal". Each deal can have "I" properties, "J" investors, "K" mortgages, and "L" credit lines, where "I" and "J" must be integers greater than zero and "K" and "L" are non-negative integers (i.e. 0 or...

Hello, I often hear the phrase "Well, since you are taking a ratio bin-by-bin, you don't have to care about the luminosity syst. uncertainty and the trigger efficiency syst. uncertainty". I think I understand qualitatively why this is the case (It cancels out in the ratio, since both...

Homework Statement The time (minute) that it takes for a terrain runner to get around a runway is a random variable X with the tightness function fX = (125-x)/450 , 95≤x≤125 How big is the probability of eight different runners, whose times are independent after 100 minutes: a) Everyone has...

Homework Statement In a vessel is a 5 cent coin and two 1-cent coins. If someone takes up two randomly chosen of these coins, and we let X be the total value of the coins taken, what is the probability function for X? Homework Equations I know that X has a value {2,6} The Attempt at a...

Hi these are practice questions from our class. can someone please help me by cheaking if i have done the correct answear ? if i am wrong could someone please provide the correct answear ? Thanks 1. The z-value that is used to construct a 95% confidence interval is A 1.28 B 1.96 C 2.58 D 1.64...

Homework Statement So I am doing a project for statistics and wanted to apply a hypothesis test to see if there is a correlation between the number of years spent at my college and the number of services used. The services include library, recreational services, clubs, etc.. i sent out a survey...

I'm trying to get into a Masters program in Statistics, and below are a few that seemed interesting. I was wondering if anyone who has any feedback, experience, or heard anything on the programs. I"m already full time employed as an analyst, so I'm not getting it to start a new career. Rather, I...

While doing some calculations on v_rms using the Maxwell-Boltzmann distribution, I noticed that v_rms and v_avg are pretty similar (https://casper.berkeley.edu/astrobaki/index.php/File:MaxwellSpeedDist.png). In fact, really it's just the choice of using the 1-norm (|v|_avg) vs. 2-norm sqrt(v^2...

I require your help to list all phenomena described as interferences in physics ( as teached nowadays ) with their citations in scholar documents if they are not well known by non-specialists. I am open to adjacent domains like information theory and mathematics. There are already light...

I was given the averages (AVG) and the corresponding standard deviation (SD) of sets of data. I have no copy of the raw data for each data point that were used to calculate the AVG and SD. I performed further data treatment on the data. I want to ask what is the relationship between the...

Homework Statement In the calculation in high temperatures of ##Z_{rot} = (\sum_{j=0}^\infty (2j+1)\exp{j(j+1)\theta_{rot}/T})^N##; they use Euler summation formula: $$\sum_{n=0}^\infty f(n) = \int_0^\infty f(x)dx+\frac{1}{2}f(0)-\frac{1}{12}f'(0)+\frac{1}{720}f^{(3)}(0)+\ldots$$ for ##f(x) =...

Homework Statement Given X_1,\dots,X_n a simple random sample with normal variables (\mu, \sigma^2). We assume \mu is known but \sigma^2 is unknown. The hypothesis is \begin{cases} H_0: & \mu=\mu_0 \\ H_1: & \mu=\mu_1 > \mu_0 \end{cases} Determine the rejection region R...

I'm having a hard time understanding 'degrees of freedom'. Could someone please provide an example in terms of Quantum Mechanics about what a 'degree of freedom' could be represented as? Is it simply a number of observations of a physical system to determine the arrangement of particles within...

Homework Statement If event A equals event B, then the probability of their intersection is 1. True or False? Apparently the correct answer is False. The Attempt at a Solution If A=B then they should overlap entirely and their intersection should be 1? The only way I see this working is if...

Homework Statement There are 22 students in a class. The professor will divide the class into 4 groups. Group 1 and 2 have 5 members each whilst Group 3 and 4 have 6. Given that the teacher forms the group at random, find the probabilities of : A = event where Paula, Trina, Gia all belong in...

Homework Statement Prove the continuity from below theorem. Homework EquationsThe Attempt at a Solution So I've defined my {Bn} already and proven that it is a sequence of mutually exclusive events in script A. I need to prove that U Bi (i=1 to infinity) is equal to U Ai (i=1 to infinity) to...

Hello, I am just posting a quick question asking what is better if I want to get into investment banking. If I was too go for statistics, I would most likely get a PhD. If I went for mathematics I would want to double major in Econ and Math and get an undergraduate degree in both. Which is a...

Hi, I'm not sure whether my understanding of this question is correct: An app predicts rain tomorrow. Recently, it has rained only 73 days each year. When it actually rains, the app correctly forecasts rain 70% of the time. When it does not rain, it incorrectly forecasts rain 30% of the time...

I apologize for the simplicity of the question (NOT homework). This is a statistical question (not necessarily a quantum mechanical one). If I have an initial probability function with an associated expected value and then a second probability function is superimposed on the initial...

I am stuck on this concept in my physics book where the author claims that in a low density ionic gas the average of the time between collision and average of the time taken from last collision in ions is same. He further states that the average time to the next collision is same as the average...

My research requires using the multilevel structural equation model (MSEM). I've read countless articles related to MSEM and I have not been able to pinpoint the best program. They vary from SPSS, MPlus, SAS, LISREL, AMOS, R2, etc. Any recommendations? I've asked around my academic circle and...

Homework Statement Prove that A(X(ωk)2)≥A(X(ωk))2 if and only if X(ωk) has the same value for every k such that pk>0 for every category which actually occurs in the population Homework Equations A(X)=1/N∑nkX(ωk)=∑pkX(ωk) The Attempt at a Solution A[(X-A(X)2)]=A(X2)-A(X)2 and i believe the...

Hi All, Currently on a distance learning HNC and I am not quite sure whether the question just wants me to answer 'yes' or give mathematical evidence. Part A answered, Part B not sure... Any help would be great! 2. The process for the production of an electrical device is suitable for...

I'm looking at this quote: "The proportions of the phyla Firmicutes and Bacteroidetes were statistically significantly increased in the obese group compared to the normal weight group (p< 0.001, p = 0.003 respectively)." Since I don't know statistics can you please explain how to visualize...

Hi all, I'm currently in the middle of performing an experiment for the final project of my MSc, and I have a question about how I should go about weighting the data when fitting a curve to it using the MATLAB fitting tool. Firstly, a bit of background about the problem. I am seeing how low...

I am looking for advanced problems in statistics with answer sheet on the subjects: probability distributions where you have to rewrite the sum of variables to a new probability distribution. Advanced problems in calculating variance and expected values for probability distributions. Advanced...