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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...

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...

$$Q_{(\alpha, \beta)} = \sum_{N=0}^{\infty} e^{\alpha N} Z_{N}(\alpha, \beta) \hspace{1cm} (3.127)$$ 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...

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...

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... $$ \prod_{n=1}^\infty \frac {d_n!} {N_n!(d_n-N_n)!}$$...

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...

Check out the full lecture on the Royal Institution YouTube channel.

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...

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)

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

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...

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...

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)! =(...

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...

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...

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...

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], ])...

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...

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...

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...

**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...

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...

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...

<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...

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...

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...

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...

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(...)...

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...