Read about statistics | 171 Discussions | Page 1

  1. D

    Rotational partition function for CO2 molecule

    Hello fellow physicists, I need to calculate the rotational partition function for a CO2 molecule. I'm running into problems because I've found examples were they say this rotational partition function is: ##\zeta^r= \frac T {\sigma \theta_r} = \frac {2IkT} {\sigma \hbar^3}## Where...
  2. G

    Confidence Interval Question help please

    Here is the question I'm struggling with (Q1) : I just... I just don't understand what my first step is. Whats my barx1 and barx2? (bar x = mean, x1 = subscript 1) My thoughts on approaching this question : barX1 - barX2 `~ N(u1-u2, sd1^2/n1 + sd2^2/n2) Find Z value when p = 0.975, z = + or...
  3. T

    Calculate the average number of oscillators of an Einstein solid, in the grand canonical ensemble, when q>>N

    $$Q_{(\alpha, \beta)} = \sum_{N=0}^{\infty} e^{\alpha N} Z_{N}(\alpha, \beta) \hspace{1cm} (3.127)$$ Where ##Q## is the grand partition function, ##Z_N## is the canonical partition function and: $$\beta = \frac{1}{kT} \hspace{1cm} \alpha = \frac{\mu}{kT} \hspace{1cm} (3.128)$$ In the case of an...
  4. Schwann

    I 'Conservative' p-values adjusted

    Hello everyone! Could anybody recommend some strategy of p-values adjustment, as the distribution of my p-values indicates the presence of a big number of false negatives? Usually p-values are adjusted in order to overcome Type 1 errors (e. g. FDR or FWER estimation), but what I need to do is...
  5. SamRoss

    I Seeking better explanation of some quantum stats formulae

    In "Introduction to Quantum Mechanics", Griffiths derives the following formulae for counting the number of configurations for N particles. Distinguishable particles... $$ N!\prod_{n=1}^\infty \frac {d^{N_n}_n} {N_n !} $$ Fermions... $$ \prod_{n=1}^\infty \frac {d_n!} {N_n!(d_n-N_n)!}$$...
  6. michaelwright

    B Fun with (im)probabilities

    Hi folks - I need some help with a tricky probability. Here's the situation: Let's say there are 4M internet users in Age Group A. (The total set) Of those 4M, there are 1,000 users who play a specific sport. Those 1,000 are spread evenly over 125 teams, so 8 players each. 1. What's the...
  7. The Parker Machine: it's 80% accurate.

    The Parker Machine: it's 80% accurate.

    Check out the full lecture on the Royal Institution YouTube channel.
  8. Cesca Roma

    I Discriminant function analysis - stepwise or otherwise?

    I’m using discriminant function analysis to determine the potential accuracy of several biometric measurements being used in conjunction for binary classification purposes for my BSc Biomed research project. Overall I've only got 110 data points so it's a stretch but hey, that's anatomy! What...
  9. BlueKaiza

    Interpreting pie and bar charts

    Working 1. a (i) 1/4=×5% (ii)120/360×100=33.3% (b) newspaper=£9000 Leaf=£6500 Transport=£19000 55000-34500=£20500 Tv=16.7% 0.167×55000=£9185 ( answer) (c) Tv=16.7% News=25% Leaf=15.3% Other=9.72% Trans=33.3%(answer) Note: they were rounded to (3sf)
  10. The Datasaurus Dozen

    The Datasaurus Dozen

    Same Stats, Different Graphs: Generating Datasets with Varied Appearance and Identical Statistics through Simulated Annealing
  11. JorgeM

    I Is this weighted mean and standard deviation correct?

    The expression I have found is this one. https://ibb.co/kqG24L3 I have been looking for information because I could not to realize what is the value that "alpha" has to have. If any of you do know what this alpha value is supposed to represent or if you have seen it before I would be really...
  12. parazit

    I Comparing theoretical calculations with experimental data

    Dear users, The situation I have encountered is a simple statistical comparison of the experimental data, which accepted as correct, with the results obtained via six theoretical models. In the experimental data, there exist y values corresponding to x values and also the measurement errors of...
  13. rhiana

    How do i answer this permutation question?

    Question: A home security device with 10 buttons is disarmed when three different buttons are pushed in the proper sequence. (No button can be pushed twice.) If the correct code is forgotten, what is the probability of disarming this device? My attempt: 10!/(10-3)! =(...
  14. P-values Broke Scientific Statistics—Can We Fix Them?

    P-values Broke Scientific Statistics—Can We Fix Them?

  15. B

    I Finding CDF given boundary conditions (simple stats and calc)

    I'm not quite sure if my problem is considered a calculus problem or a statistics problem, but I believe it to be a statistics related problem. Below is a screenshot of what I'm dealing with. For a) I expressed f(t) in terms of parameters p and u, and I got: $$f(t)=\frac{-u \cdot a + u \cdot...
  16. mPlummers

    Relative error and measurement precision

    NOTE: this is a programming exercise (Python). I started adding to ##x_{true}## an error related to a (for example) 10% relative error, obtaining ##x_{measurement}##. Then i computed ##y_{measurement}##. To find the precision, i calculated ##(y_{true}-y_{measurement})/y_{measurement}##. If it is...
  17. olgerm

    I Standard deviation question -- population std vs sample std

    I know that standard deviation of whatever data is defined as sqaure root of square difference from mean value: ##\sigma(data)=\frac{\sum_{x \in data}((x-x_{mean\ of\ data})^2)}{|data|}=\frac{\sum_{x \in data}((x-\sum_{y \in data}(y)/|data|)^2)}{|data|}## but sometimes formula...
  18. user366312

    Finding conditional and joint probabilities from a table of data

    Let, alpha <- c(1, 1) / 2 mat <- matrix(c(1 / 2, 0, 1 / 2, 1), nrow = 2, ncol = 2) chainSim <- function(alpha, mat, n) { out <- numeric(n) out[1] <- sample(1:2, 1, prob = alpha) for(i in 2:n) out[i] <- sample(1:2, 1, prob = mat[out[i - 1], ])...
  19. Badgun

    Impact of several variables on resulting projectile motion trajectory

    I was told to generate these variables (m, C, alpha, wind velocity) normally distributed and compare the random data with the result and then tell, which of the variables has the most impact. Here I am stuck, tried to compare variances, kurtosis and skewness of the data (the original variables...
  20. caters

    Are my calculations of the pregnancy ratio of the population correct?

    Monthly Cycle numbers Here is the cycle ratio: $$2_{early}:2_{fertile}:1_{late}$$ And the numbers: $$20,000_{early}:20,000_{fertile}:10,000_{late}$$ Now, let's divide the early into 2 groups, pre-fertile, and safe and assume there is a 50/50 split between those 2 groups. Let's also assume...
  21. J

    Chi-squared test for normality

    Homework Statement Hello, I was given 2 sets of data, showing 20 temperature values and 35 temperature values respectively. The data sets look like below: Data 1 Data 2 Temperature Temperature 30.9...
  22. iVenky

    Power of noise after passing through a system h(t)

    **Reposting this again, as I was asked to post this on a homework forum** 1. Homework Statement Hi, I am trying to solve this math equation (that I found on a paper) on finding the variance of a noise after passing through an LTI system whose impulse response is h(t) X(t) is the input noise...
  23. J

    Math/Statistics PHD Application

    I Know this is prob the wrong site to post this but... Hello, I am a student at a low-ranked college in New York State actively pursuing a bachelors (BA) in Math in my junior year. I have a 3.7 GPA overall and a 3.73 in Math. I am looking to apply to PHD programs next year in Statistics or in...
  24. iVenky

    I White noise & 1/f noise after a system h(t)

    Hi, I am trying to solve this math equation on finding the variance of a noise after passing through a system whose impulse response is h(t) X is the input noise of the system and Y is the output noise after system h(t) if let's say variance of noise Y is σy2=∫∫Rxx(u,v)h(u)h(v)dudv where...
  25. J

    B How to Present Statistical Data

    <Moderator's note: Moved from a homework forum.> Mass (g) +/- 0.01 grams Drop height (centimeters) +/- 3.00 Shell 53.47 45 No crack 56.78 45 Cracked...
  26. CivilSigma

    Characteristic Function Integrand Evaluation

    Homework Statement [/B] I am trying to determien the characteristic function of the function: $$ f(x)= ae^{-ax}$$ $$\therefore E(e^{itx}) =\int_0^\infty e^{itx}ae^{-ax} dx = a \cdot \frac{e}{it-a} |_0 ^ \infty $$ But I am not sure how to evaluate the integral. Wolfram alpha suggests this...
  27. JackLee

    How to read a joint discrete table?

    Homework Statement [/B] Given a group of 100 married couples, let X1 be the number of sons and X2 the number of daughters the couple has. P(X1 = 0, X2 = 2) = f(0, 2) = 8 /100 = 0.08 2. Homework Equations The Attempt at a Solution I tried to look for a similar example online, I found this...
  28. T

    Showing Rejection Region Equality with Fisher Distribution

    Homework Statement [/B] For reference: Book: Mathematical Statistics with Applications, 7th Ed., by Wackerly, Mendenhall, and Scheaffer. Problem: 10.81 From two normal populations with respective variances ##\sigma_1^2## and ##\sigma_2^2##, we observe independent sample variances ##S_1^2## and...
  29. R

    I Principal component analysis (PCA) coefficients

    I am trying to use PCA to classify various spectra. I measured several samples to get an estimate of the population standard deviation (here I've shown only 7 measurements): I combined all these data into a matrix where each measurement corresponded to a column. I then used the pca(...)...
  30. Dewgale

    Anti-commutation of Dirac Spinor and Gamma-5

    Homework Statement Given an interaction Lagrangian $$ \mathcal{L}_{int} = \lambda \phi \bar{\psi} \gamma^5 \psi,$$ where ##\psi## are Dirac spinors, and ##\phi## is a bosonic pseudoscalar, I've been asked to find the second order scattering amplitude for ##\psi\psi \to \psi\psi## scattering...
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